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## 18 Types of Diagrams You Can Use to Visualize Data (Templates Included)

Have you ever found yourself stuck while trying to explain a complex concept to someone? Or struggling to put your idea into words?

This is where diagrams come in.

While simple text is best for highlighting figures or information, diagrams are handy for conveying complex ideas and loads of information without overwhelming your audience. They can visualize almost anything, from numerical data to qualitative relationships, making them versatile tools in numerous fields.

Whether you’re in the academe or enterprise setting, this guide is for you. We’ll explore the different types of diagrams with a brief explanation for each type, the best time to use a diagram type, and how you can use them to be a better visual storyteller and communicator. You’ll also find examples and templates for each type of diagram.

Let’s get on with it.

You can also follow along by creating a free account . Select a template to get started.

## What exactly is a diagram?

A diagram is a visual snapshot of information. Think of diagrams as visual representations of data or information that communicate a concept, idea, or process in a simplified and easily understandable way. You can also use them to illustrate relationships, hierarchies, cycles, or workflows.

Diagrams aren’t just used to show quantitative data, such as sales earnings or satisfaction ratings with a diagram. They’re equally helpful if you want to share qualitative data. For example, a diagram could be used to illustrate the life cycle of a butterfly, showcasing each transformation stage.

Now, let’s jump into the various types of diagrams, ranging from simple flow charts to the more complex Unified Modeling Language (UML) diagrams.

## 18 diagram types and when to use each type

Whether you’re doing data analysis or need a simple visual representation of data, there is a wide array of diagrams at your fingertips. If you’re having a hard time choosing the right diagram for your data visualization needs, use the list below as a quick guide.

## 1. Flowchart

A flowchart is a type of diagram that acts as a roadmap for a process or workflow. It uses shapes and arrows to guide you through each step, making complex procedures simple to understand.

Flowcharts are best for : Simplifying complex processes into understandable stages, making it easier for your readers to follow along and see the ‘big picture”.

## 2. Line graph

Line graphs , sometimes called line charts, visualizes numerical data points connected by straight lines. In a line graph or line chart, data points representing different time periods are plotted and connected by a line. This helps with easy visualization of trends and patterns.

Line graphs are best for: Representing the change of one or more quantities over time, making them excellent for tracking the progression of data points.

## 3. Bar chart

A bar chart , often interchangeable with bar graphs, is a type of diagram used primarily to display and compare data. For this diagram type, rectangular bars of varying lengths represent data of different categories or groups. Each bar represents a category, and the length or height of the bar corresponds to the numeric data or quantity.

Variations of bar charts include stacked bar charts, grouped bar charts, and horizontal bar charts.

Bar charts are best for : Comparing the frequency, count, or other measures (such as average) for different categories or groups. A bar chart is particularly useful if you want to display data sets that can be grouped into categories.

## 4. Circle diagram or pie chart

A pie chart is a circular diagram that represents data in slices. Each slice of the pie chart represents a different category and its proportion to the whole.

Pie charts are best for: Displaying categorical data where you want to highlight each categoryâs percentage of the total.

## 5.Venn diagrams

A Venn diagram compares the differences and similarities of groups of things. As a diagram based on overlapping circles, each circle in a Venn diagram represents a different set, and their overlap represents the intersection of the data sets.

Venn diagrams are best for : Visualizing the relationships between different groups of things. They are helpful when you want to show areas of overlap between elements. A good example is if you want to compare the features of different products or two overlapping concepts, like in the Ikigai Venn diagram template below. Easily create your Venn diagram with Piktochart’s online Venn diagram maker .

## 6. Tree diagrams

A tree diagram is a diagram that starts with one central idea and expands with branching lines to show multiple paths, all possible outcomes, decisions, or steps. Each ‘branch’ represents a possible outcome or decision in a tree diagram, moving from left to right. Tree diagrams are best for : Representing hierarchy like organizational roles, evolutionary relationships, or possible outcomes of events like when a company launches a product.

## 7. Organizational chart

Organizational charts are diagrams used to display the structure of an organization. In an organizational chart, each box or node represents a different role or department, and lines connecting the boxes illustrate the lines of authority, communication, and responsibility. The chart typically starts with the highest-ranking individual or body (like a CEO or Board of Directors) at the top and branches downwards to various levels of management and individual employees.

Organizational charts are best for : Showing relationships between different members and departments in a company or organization.

## 8. Gantt charts

Gantt charts are typically used in project management to represent the timeline of a project. They consist of horizontal bars, with each bar representing a task or activity.

For this type of diagram, each chart is represented by a horizontal bar spanning from its start date to its end date. The length of the bar corresponds to the duration of the task. Tasks are listed vertically, often in the order they need to be completed. In some projects, tasks are grouped under larger, overarching activities or phases.

Gantt charts are best for : Projects where you need to manage multiple tasks that occur over time, often in a specific sequence, and may depend on each other.

## 9. Unified Modeling Language (UML) diagram

Software engineers use Unified Modeling Language (UML) diagrams to create standardized diagrams that illustrate the building blocks of a software system.

UML diagrams, such as class diagrams, sequence diagrams, and state diagrams, provide different perspectives on complex systems. Class diagrams depict a system’s static structure, displaying classes, attributes, and relationships. Meanwhile, sequence diagrams illustrate interactions and communication between system entities, providing insight into system functionality.

UML diagrams are best for : Visualizing a software system’s architecture in software engineering.

## 10. SWOT analysis diagrams

A SWOT analysis diagram is used in business strategy for evaluating internal and external factors affecting the organization. The acronym stands for Strengths, Weaknesses, Opportunities, and Threats. Each category is represented in a quadrant chart, providing a comprehensive view of the business landscape.

SWOT diagrams are best for : Strategic planning and decision-making. They represent data that can help identify areas of competitive advantage and inform strategy development.

Piktochart offers professionally-designed templates to create diagrams , reports , presentations , brochures , and more. Sign up for a free account today to create impressive visuals within minutes.

## 11. Fishbone diagram

Fishbone diagrams, sometimes called cause-and-effect diagrams, are used to represent the causes of a problem. They consist of a central idea, with different diagrams or branches representing the factors contributing to the problem.

Fishbone diagrams are best for : Brainstorming and problem-solving sessions.

## 12. Funnel chart

A funnel chart is a type of diagram used to represent stages or progress. In a funnel chart, each stage is represented by a horizontal bar, and the length of the bar corresponds to the quantity or value at that stage. The chart is widest at the top, where the quantity or value is greatest, and narrows down to represent the decrease at each subsequent stage.

Funnel charts are best for: Visual representation of the sales pipeline or data visualization of how a broad market is narrowed down into potential leads and a select group of customers.

## 13. SIPOC diagrams

A SIPOC diagram is used in process improvement to represent the different components of a process. The acronym stands for Suppliers, Inputs, Process, Outputs, and Customers.

SIPOC diagrams are best for: Providing a high-level view of a process which helps visualize the sequence of events and their interconnections.

## 14. Swimlane diagrams

Swimlane diagrams are best for mapping out complex processes that involve multiple participants or groups.

Keep in mind that each lane (which can be either horizontal or vertical) in a swimlane diagram represents a different participant or group involved in the process. The steps or activities carried out by each participant are plotted within their respective lanes. This helps clarify roles and responsibilities as well as the sequence of events and points of interaction.

Swimlane diagrams are best for : Visualizing how different roles or departments interact and collaborate throughout a workflow or process.

## 15. Mind maps

A mind map starts with a central idea and expands outward to include supporting ideas, related subtopics, concepts, or tasks, which can be further subdivided as needed. The branches radiating out from the central idea represent hierarchical relationships and connections between the different pieces of information in a mind map.

Mind maps are best for : Brainstorming, taking notes, organizing information, and visualizing complex concepts in a digestible format.

## 16. Scatter Plots

Scatter plots are used to compare data and represent the relationship between two variables. In a scatter plot, each dot represents a data point with its position along the x and y axes representing the values of two variables.

Scatter plots are best for : Observing relationships and trends between the two variables. These scatter plots are useful for regression analysis, hypothesis testing, and data exploration in various fields such as statistics, economics, and natural sciences.

## 17. PERT chart

PERT (Project Evaluation Review Technique) charts are project management tools used to schedule tasks. Each node or arrow represents each task, while lines represent dependencies between tasks. The chart includes task duration and earliest/latest start/end times.

Construction project managers often use PERT charts to schedule tasks like design, site prep, construction, and inspection. Identifying the critical path helps focus resources on tasks that impact the project timeline.

PERT charts are best for : Visualizing the sequence of tasks, the time required for each task, and project timelines.

## 18. Network diagrams

A network diagram visually represents the relationships between elements in a system or project. In network diagrams, each node represents an element, such as a device in a computer network or a task in a project. The lines or arrows connecting the nodes represent the relationships or interactions between these elements.

Network diagrams are best for: Visually representing the relationships or connections between different elements in a system or a project. They are often used in telecommunications, computer networking, project management, and organization planning.

## Choosing the right diagram starts with a good understanding of your audience

Understanding your audience’s needs, expectations, and context is necessary before designing diagrams. The best diagram is not the one that looks the most impressive but the one that communicates complex information most clearly and effectively to your intended audience.

Make professional diagrams for free with no design experience with Piktochart’s online diagram maker . Sign up for free .

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## Diagrammatic Presentation Of Data

Introduction.

The diagrammatic representation also helps in having a birdâs eye view or overall view of the differentiation of data. It is a norm to present statistical data in the form of diagrams so that it becomes easier to comprehend and understand them. Therefore, diagrammatic representation is an important tool in statistics.

## What is a Diagrammatic Presentation of Data?

Diagrammatic representation refers to a representation of statistical data in the form of diagrams. The diagrams used in representing statistical data are geometrical figures, such as lines, bars, and circles. The intention of using geometrical figures in statistical presentation is to make the study more interesting and easy to understand. Diagrammatic representations are widely used in statistics, economics, and many other fields of study.

## Types of Diagrammatic Presentations of Data

Various types of diagrammatic representations of data depend on the dataset and the particular statistical elements in them. Data presentation can be made in different types and forms.

These can be broadly classified into the following one-dimensional types â

## Line Diagram

In a line diagram, straight lines are used to indicate various parameters. Here, a line represents the sequence of data associated with the changing of a particular variable.

Properties of Line Diagram â

The Lines are either in vertical or horizontal directions.

There may be uniform scaling but this is not mandatory.

The lines that connect the data points offer the statistical representation of data.

The following is an example of a line diagram that shows profits in Rs crore from 2002 till 2008. Profit in 2002 was Rs 5 Crore while in 2008 it was Rs 24 Crore.

## Bar Diagram

Bar diagrams have rectangular shapes of equal width that represent statistical data in a straightforward manner. Bar diagrams are one of the most widely used diagrammatic representations.

Properties of Bar Diagram â

The Bars can be vertical or horizontal in directions.

All bars in a diagram have a uniform width.

All the Bars have a common and same base.

The height or width of the Bar shows the required value.

The following is an example of a Bar Chart that has time on the X axis and profits on the Y axis.

Also known as a "circle chart" , the pie chart divides the circular statistical graphic into sectors or sections to illustrate the numerical data. Each sector in the circle denotes a proportionate part of the whole. Pie-chart works the best at the time when we want to denote the composition of something. In most cases, the pie chart replaces other diagrammatic representations, such as the bar graph, line plots, histograms, etc.

In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

## Advantages of Diagrammatic Presentation of Data

Easier to understand.

Pictorial representations are usually easier to understand than statistical text or representation in tabular form. One can easily understand which portion or part has more contribution toward the overall dataset. This helps in understanding the data better.

The creators of diagrams usually keep the simplicity of presentation in mind to offer more information to readers. That is why diagrams are easier to comprehend than texts and tables.

## More attractive

Pictorial or diagrammatic representations of datasets are more attractive than normal representations. As colors and various other tools can be incorporated into diagrams, they become more attractive and comprehensible for the readers.

Moreover, as diagrams can be made more interactive with the help of computer graphics, they have become more acceptable and attractive currently.

## Simpler presentations

Data can be presented more simply in diagrammatic form. Both extensive unstable data and smaller complex data can be represented by diagrammatic representations more easily. This helps statisticians offer more value to their findings.

## Comparison is easier

When two or more data are compared, it is easier to do so in pictorial form. As diagrams clearly show the portion of data consumed, it can be easily understood from the diagrams which part of the data is consuming more area in the diagrams. This can help one to understand the real differences through pictorial comparison.

## Universal acceptance

Diagrammatic representation of data is used in many fields of study, such as statistics, science, commerce, economics, etc. So, the diagrams are accepted universally and hence are used everywhere.

Moreover, since there are the same procedures for forming diagrams, the representations mean the same thing to everyone. So, there is nothing to alter when we obtain the diagrams to check the real values. It helps analysts solve problems universally.

## Improvement in presentation

Diagrammatic representations improve the overall representation of data to a large extent. As the data is classified into several groups and presented in a systematic manner in diagrams, the whole presentation of data gets improved during the diagrammatic representation.

Moreover, as diagrams can be made more interactive than texts or tables, diagrammatic presentations are one step ahead in presenting the data in a simpler yet recognizable manner.

## More organized and classified data

To represent data in diagrams, they must be organized and classified into comprehensive categories. This helps the data to be organized in a given fashion which makes them orderly and creates a sequence. This in turn helps realize diagrammatic data better than text forms.

## Relevance Diagrammatic Presentation of Data

Diagrams are a great way of representing data because they are visually attractive and they can make large, complex datasets look simpler. The otherwise heavy data can be simply and easily represented by line and bar diagrams, and pie charts. This makes data organization simpler and neater.

Moreover, as data must be classified before representation, one must organize them according to the norms required. So, diagrammatic representations save lots of time and resources.

Diagrams also have universal acceptance and so can be used to express data in different forms. This provides the analysts and researchers flexibility to present data in any required form.

Diagrams also remove confusion and offer a simpler tactic to present data. As no special skill has to be learned to represent data in diagrams, they can be used by most to show statistical data and results of various types of research and experiments.

Therefore, diagrammatic representation has great relevance that can be used for the benefit of economists, statisticians, marketing analysts, and a lot of other professionals.

The diagrams are a central part of statistics and their importance can be known from the fact that almost all statistical researchers use them in one way or the other. The diagrammatical representations make inferring statistical data much simpler and easier. It is a much easier way to visualize and understand data in simpler forms too.

To represent data in diagrammatic form, only a simple understanding of Mathematics is required. So, no special skills are needed to use diagrams and this makes them very popular tools for the representation of data sets. Learning how to present data in diagrams, therefore, should be a priority for everyone.

Q1. Which is the simplest diagrammatic presentation of data?

Ans. The simplest diagrammatic presentation of data is a line diagram that shows data in terms of straight lines.

Q2. What are the two characteristics of bar diagrams?

Ans. Bar diagrams have uniform width and their base remains the same.

Q3. How are the sections in a pie chart formed?

Ans. In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

For example, if a section requires 25% of the presentation, it will consume degrees on the chart.

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- Diagrammatic Presentation of Data

Nowadays a lot of emphases is laid upon exceptional presentation of data.Â All of this is because, when presented diagrammatically, data is easy to interpret with just a glance. In such a case we need to learn how to represent data diagrammatically via bar diagrams, pie charts etc.

## Suggested Videos

Bar diagrams.

As the name suggests, when data is presented in form of bars or rectangles , it is termed to be a bar diagram.

## Features of a Bar

- The rectangular box in a bar diagram is known as a bar. It represents the value of a variable .
- These bars can be either vertically or horizontally arranged.
- Bars are equidistant from each other.
- Each bar originates from a common baseline or a common axis.
- The width of bars remain same but the height changes, according to the value of a variable, to denote the difference between their values.
- Unless they are in a specific order, the convention is that bars can be arranged in an ascending or descending order.

## Browse more Topics under Presentation Of Data

- Textual and Tabular Presentation of Data

## Types of Bar Diagrams

Simple bar diagram.

These are the most basic type of bar diagrams. A simple bar diagram represents only a single set of numerical data. Generally, simple bar diagrams are used to represent time series data for a single entity.

Generally, the Y-axis contains markings which represent the range of the value of variable whereas the X-axis contains divisions for entities like years, time periods, areas etc.

## Multiple Bar Diagram

Unlike single bar diagram, a multiple bar diagram can represent two or more sets of numerical data on the same bar diagram. Generally, these are constructed to facilitate comparison between two entities like average height and average weight, birth rates and death rates etc.

Separate sets of numerical data are differentiatedÂ with the help of colour variation. By the same token of simple bar diagrams, multiple bar diagrams also have divisions on Y-axis and X-axis that represent different values of the variable and entities like year, areas etc. respectively. Note that each division on X-axis has two or more bar diagrams each according to the specified number of bars.

## Sub-divided or Differential Bar Diagrams

Sub-divided bar diagrams are useful when we need to represent the total values and the contribution of various sections of the total simultaneously. The different sections are shaded with different colours in the same bar.

For example, such a bar diagram can be used to represent the varying levels of employment over the years in India and each bar can be divided into two sectors, the urban and rural. Again, here the Y-axis and X-axis represent same values as in simple and multiple bar diagrams.

## Percentage Bar Diagrams

This is derived further from the subdividedÂ bar diagrams. In this, each bar has the same heightÂ that represents 100 percent of the Y-axis in totality. Further, each bar is divided into sections based on percentages calculated according to the contribution of these sections.

Percentage bar diagrams are used when the values are really high. This is because using subdivided bar diagrams in such cases would not be easy and appropriate.

## Deviation Bar Diagrams

Lastly, the deviation bar diagrams are most interesting of the lot. In such a type of bar diagram, there are both negative and positive values on the y-axis. The deviation bar diagrams are used to compare the net deviation of related variables with respect to time and location.

For example, it can be used to represent a bar diagram for savings (represented by positive deviations) and deficit (represented by negative deviations) over years.

## Pie or Circular Diagrams

In addition to bar diagrams, pie diagrams are also widely used to pictorially represent data. In this, a circle is divided into various segments which are decided on the basis of percentages. Which means the circle is divided into sectors depending on various percentages.

These sectors are differentiated with the help of colours. Pie diagrams have an edge over bar diagrams because they can easily provide an overview and provides a better sense of contributions of each part. The steps for construction of a pie diagram are:

The first step involves finding out respective percentages. This is done by a simple mathematical formula to find out percentages which is –

{(Parts for the respective sector)/total parts)Â Ă100} .

For example, if in a class of 1oo students, 30 are obese, 20 are fat and 50 are slim then the percentages will be as follows:

(30/100) Ă 100= 30%

(20/100) Ă 100= 20%

(50/100) Ă 100= 50%

2] A circle comprises 360 degrees. The angles that each sector will span across is decided by the given formula: (Percentage value/100)Ă360Â°

3] Finally, just plot these values according to their respective angles on a circle and give appropriate markings to complete the pie chart.

## A Solved Example for You

Q: Â Which among the following is not a feature of a bar in the bar diagram?

- The width is same but the heights are generally different
- They are rectangular in shape
- Bars should not be equidistant
- Each bar originates from a common baseline

Ans: Â Of all the above options, option C is incorrect because conventionally the bars should be equidistant.

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## Presentation of Data

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## Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

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## Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

## Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

## Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

## Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

- It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
- It can be used in almost all fields from mathematics to physics to psychology and so on.
- It is easy to understand for its visual impacts.
- It shows the whole and huge data in an instance.
- It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

## Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

- Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
- Measurement Unit: The measurement unit in the graph should be mentioned.
- Proper Scale: A proper scale needs to be chosen to represent the data accurately.
- Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
- Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
- Simple: The construction of a graph should be easily understood.
- Neat: The graph should be visually neat in terms of size and font to read the data accurately.

## Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

## Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Data Representation | Description |
---|---|

A group of data represented with rectangular bars with lengths proportional to the values is a . The bars can either be vertically or horizontally plotted. | |

The is a type of graph in which a circle is divided into Sectors where each sector represents a proportion of the whole. Two main formulas used in pie charts are: | |

The represents the data in a form of series that is connected with a straight line. These series are called markers. | |

Data shown in the form of pictures is a . Pictorial symbols for words, objects, or phrases can be represented with different numbers. | |

The is a type of graph where the diagram consists of rectangles, the area is proportional to the frequency of a variable and the width is equal to the class interval. Here is an example of a histogram. | |

The table in statistics showcases the data in ascending order along with their corresponding frequencies. The frequency of the data is often represented by f. | |

The is a way to represent quantitative data according to frequency ranges or frequency distribution. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf. | |

Scatter diagram or is a way of graphical representation by using Cartesian coordinates of two variables. The plot shows the relationship between two variables. |

## Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

- x and y graph
- Frequency Polygon
- Cumulative Frequency

## Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360Âș as result. â 2x + 8x + 10x = 360Âș â 20 x = 360Âș â x = 360Âș/20 â x = 18Âș Therefore, the value of x is 18Âș.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Stem | Leaf |

1 | 2 4 |

2 | 1 5 8 |

3 | 2 4 6 |

5 | 0 3 4 4 |

6 | 2 5 7 |

8 | 3 8 9 |

9 | 1 |

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values Ă· 19 = 958 Ă· 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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## Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

## What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

- Stem and leaf plot
- Scatter diagrams
- Frequency Distribution

## Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

## What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

## What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

## What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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- Diagrammatic Presentation of Data

## Introduction - Diagrammatic Presentation of Data

Diagrams are an essential operational tool for the presentation of statistical data. They are objects, mainly geometrical figures such as lines, circles, bars, etc. Statistics elaborated with the help of diagrams make it easier and simpler, thereby enhancing the representation of any type of data.

## What is Diagrammatic Representation of Data?

Representation of data assisted by diagrams to increase the simplicity of the statistics surrounding the concerned data is defined as a diagrammatic representation of data. These diagrams are nothing but the use of geometrical figures to improve the overall presentation and offer visual assistance for the reader.

## What are the Types of Diagrams used in Data Presentation?

The type of diagram suitable for data presentation solely depends on the particular dataset and its statistical elements. There are multiple types of diagrams used in data presentation. They can be broadly categorized in the following types of one-dimensional diagrams â

## A. Line Diagram

Line diagram is used to represent specific data across varying parameters. A line represents the sequence of data connected against a particular variable.

## Properties of Line Diagram â

The Lines can be used in vertical and horizontal directions.

They may or may not have uniform scaling

The line connecting the data points state the statistical representation of data.

Example: Arjun, Sayak and Mainak started monitoring their time of reporting for duty for a certain week. A-Line diagram to represent their observed data on average reporting time for those days would look like â

(Image will be Uploaded Soon)

So, as per the Line Diagram, it can be easily determined that Arjun reported for work mostly at 9:30 AM while Sayak and Mainakâs most frequent times of entry at work is 10:30 AM and 10:50 AM respectively.

## B. Bar Diagram

Bar Diagram is used mostly for the comparison of statistical data. It is one of the most straightforward representations of data with the use of rectangular objects of equal width.

## Properties of Bar Diagram â

The Bars can be used in vertical and horizontal directions.

These Bars all have a uniform width.

All the Bars have a common base.

The height of the Bar usually corresponds to the required value.

Example: A dataset comparing the percentile marks obtained by Shreyasi and Monika in Science subjects in the examination can be represented with the help of a Bar diagram as â

From this diagram, we can easily compare the percentile marks obtained by Shreyasi and Monika in the subjects Mathematics, Physics, Chemistry and Computer Science.

## C. Pie Chart

To know what a Pie Diagram is, it is advised to brush up on the fundamentals of the geometrical theories and formula of a Circle. For the statistical representation of data, the sectors of a circle are used as the data points of a particular dataset. A sector is the area of a circle formed by the several divisions done by the radii of the same circle.

Example: In a recent survey, a dataset was created to figure how many participants of the survey thought that Tenure or Tenor is the correct spelling in the field of Banking . A Pie Chart would present the collected data as â

With the help of this Pie Chart, it can be easily determined that the percentage of participants in the survey who chose âTenorâ, to be the correct spelling of the word for use in the field of banking, is 25% whereas 45% picked âTenureâ as the correct answer. 20% opted for both to be correct while 10% of them were not sure with their attempt.

## Advantages of Diagrammatic Presentation

There are several advantages in the presentation of data with the various types of diagrams. They are â

## 1. Makes it Much Easier to Understand

The presentation of data with the help of diagrams makes it easier for everybody to understand, which thereby makes it easier to grasp the statistics behind the data presented. Diagrammatic data presentation is quite common in newspapers, magazines and even in advertising campaigns so that the common mass can understand what the data is trying to reveal.

## 2. Presentation is Much Simpler

With the help of diagrams, presentation of extreme values â extensive unstable data as well as small complicated data complex can be simplified exponentially.

## 3. Comparison Operations are More Interactive

Datasets that require comparison of their elements use the application of diagrams for representation. Not only is the presentation attractive, but it is also ideal for showcasing a comparison in statistics.

## 4. Accepted Universally

Every academic and professional field, let it be Economics, Commerce, Science, Engineering, Statistics, etc. make use of diagrams across the world. Hence, this metric of data presentation is universally accepted.

## 5. Improves the Representation of Data as a Whole

Statistics are incomplete if diagrams are tables that are not implemented for the presentation of data. Hence, the use of diagrams helps in the overall statistical concept of data representation.

Students who are looking forward to diving deep into the theories and principles of Diagrammatic representation of data, make sure to visit the official website of Vedantu and join a live online tutoring class!

## Relevance of Diagrammatic Presentation of Data

Diagrams are visually pleasing and are a great way of representing any form of data. The heavy statistics that we generate can be easily represented via diagrams such as bar charts, pie charts etc. It makes the presentation look neater and more organized. They visually aid the reader in understanding the exact situation and are also very easy to look at. They save a lot of time and confusion and have a universal utility . All students must learn how to represent data through diagrams so that they can present facts and figures in an organized manner.

## Does Vedantu have Anything on the Diagrammatic Presentation of Data?

Vedantu has ample study material on the diagrammatic representation of data. All students can read from Diagrammatic Presentation of Data and know more. This is available completely free of cost on the platform so that the students do not hesitate before accessing them.

## FAQs on Diagrammatic Presentation of Data

1. Which are the types of diagrams used in data representation?

The types of diagrams used in the representation of data are line diagrams, bar diagrams, pie charts and a few others. These are used to represent facts as they make it easier for the students to understand certain information. More about this has been explained in the Diagrammatic Presentation of Data. This page has relevant information that the students can use to understand these diagrams. After having gone through this page, they will know how to represent certain information in the form of diagrams.

2. Are there any merits of the diagrammatic representation of data?

There are a couple of merits of the diagrammatic representation of data. Some of which is that it makes it much easier to understand data, the presentation is simpler, it becomes easier to compare and correlate, and it is universally accepted.Â

This page has all the details that are needed by the students to know. It is always better to present data in the form of diagrams as it makes it much more systematic. An organized manner of depicting figures makes anything simpler to understand.Â

3. Is a pie chart an accurate way of representing data diagrammatically?

In a pie chart, the sectors of a circle are used as the data points of a particular dataset. It is indeed an accurate method of representing data as the correct percentage can be found out. All students can check out the Diagrammatic Presentation of Data on Vedantu. This page has all the information thatâs needed by the participants. The other forms of diagrams that can be utilized for data presentations have also been talked about. This page has been created by expert Commerce teachers who know the topic inside out and can be read by all those who wish to do well in the tests.

4. Difference between the Diagrammatic and Graphical Presentation of Data.

All graphical representations of data can be a diagram, but all diagrams are not a graph. Graphs are represented on a scale, but diagrams are required to be constructed to a scale. Construction of graphs requires two more axes, but none is a necessity in case of diagrams.

5. What are the different Types of Diagrams in Statistics?

The different types of diagrams used in statistics are line diagram, bar diagram, and pie chart. Bar diagrams can further be classified into simple bar diagrams, multiple bar diagrams and component or sub-divided bar diagrams.

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## 4 Diagrammatic and Graphical Representation of Data I

Dr. Harmanpreet Singh Kapoor

Â Learning Objectives

- Introduction.
- Frequency Distribution
- Use of Diagrammatic and Graphical Presentation of the Data
- Suggested Readings

Â Â 1. L earning Objectives

In this module, a complete explanation about different types of diagrammatic representation of data will be discussed. This module helps one to learn different methods of diagrammatic presentation and their properties. Through this module, one can learn about which method of representation is appropriate under what type of conditions. Questions with answers are included to give an in-depth knowledge of the topic.

2. Â Introduction

Statistics is a science that is based on description of data either numerically or diagrammatic or other way. This science is used to extract information from the data based on the objective. Data can be in quantitative form as well in qualitative form. Data are collected from the resources of study and are available in raw form. After collecting and editing the data the next stage is to organize the data. Classification and tabulation of the data are among the most important tools for the precise, clear and comprehensible representation of the data. However, sometimes these forms of presentation are not appealing to the common person. Due to technicality involved in these forms, it may not be interesting for a common person to be able to understand the things in a simple manner. Another way to represent the data is through diagram and graphs that present the data into attractive manner that appeal more to the mind of the spectators. These forms are more attractive, fascinating and impressive than the other methods. The best part of diagrammatic representation method is that even a layman person can understand this without any previous knowledge of statistics. This is the reason that diagrams and graphs are used to give basic education to the kids.

Another important feature of the diagrammatic and graphical representation is that it saves lot of time as these are easy to build up and one can draw meaningful inference from them. These methods are able to present that information that might be lost amid the details of classification and tabulation of data. These methods also facilitate the person for comparing the value of two or more sets of data. Graphs and charts are used to clarify a complex problem and reveal the hidden facts that are not clear from the tabular form. Hence, graphs and diagrams are important not only for the representation of the data but for visual comparison of two or more datasets. Now in the next section, a brief introduction about frequency distribution and how to form it will be discussed.

Â Â 3.Â Frequency Distribution

In English language, frequency means the rate of occurrence of something in a repetitive manner in a particular time interval or time frame. Statistics is concerned with the extraction of information from the numbers collected in a raw form from the study. We already discussed about definition of variables in the second module.

In practical life, variables are used to represent these numbers in case of quantitative data like in a study of sales of luxury cars in a particular region in a year. One can consider âthe sale of a car in a dayâ as a variable and note down the sale of a car in a day by variable where i=1,2,âŠ..365. Here the values, 1, 2, âŠ . . 365 represent the sales of a car in the first day of a year or financial year and similarly second day of the year and so on. The values of 1, 2, âŠ . , 365 are known as the values of the variable.

Frequency of a value of the variable means the number of times a same value is repeated in the whole dataset. For example, if we assume that the no. of sales of a car are 2 units on 10th day, 3 units on 20th day, 2 units on the 45th day, 4 units on the 70th day of the year and so on. Here, 2 units appear two times, 3 and 4 units appear single time from the available information. So, from the available information the frequency of sale of 2 cars per day is two and other has only one. With an increase in the available information, one can construct frequency table that represent the repetition of the values in a dataset.

For example, let us consider the observation of sales of car in the month of February (28 values). These are 2, 3, 1, 2, 4, 5, 3, 2, 1, 3, 5, 6, 1, 2, 4, 2, 3, 5, 1, 3, 4, 2, 3, 5, 4, 1, 4, 2

Observations | Frequency |

1 | 5 |

2 | 7 |

3 | 6 |

4 | 5 |

5 | 4 |

6 | 1 |

Total | 28 |

Table No. 1

In the above table, we observe that for seven days two units of cars are sold, for six days three cars are sold and so on. Hence one can form the frequency table by counting the same observations in the data set this means frequency of a value of a variable is the number of times it occurs in a given series of observations. The table that represents the frequency of the value side by side is called frequency table . There are two forms of frequency distributions- Ungrouped frequency distribution and Grouped frequency distribution.

To understand the difference between two methods, we consider a data set of IQ score of 30 students and construct ungrouped and grouped frequency distribution.

Table No. 2

3.1 Ungrouped Frequency Distribution

Ungrouped frequency distribution table shows the frequency of the values in the dataset on individual basis. Table no. 3 is an example of ungrouped frequency distribution as the first column in the table represents the observations and second column shows corresponding frequency.

From Table No. 3, one can observe that 2nd column and 4th column show the frequency values of the dataset (from Table No. 2). Hence in ungrouped frequency distribution, the values of the dataset are shown on individual basis.

3.2 Group Frequency Distribution

In this method, the values of the variables are shown in the group or interval. In the following table, observations from Table no. 2 are used to present them in group frequency distribution. The smallest observation in the dataset is 35 and maximum value is 94. In Table no. 4, we consider width of the interval as 10 and lowest class value as 30 and so on till we cover the maximum value in the dataset. In the next section, we will discuss about how to choose, type of class, class interval, width of class interval etc.

From Table No. 4, we can see 70-80, 80-90 intervals have maximum frequency value that is 8. Hence we can conclude that IQ score of the most of the students lie between70 to 90.

On the comparison of Table No. 3 and Table No. 4, one can see that group frequency distribution visualize the important characteristics of the data in a simple and understandable manner about the tendency of IQ score of students over ungrouped frequency distribution.

Steps for forming a group frequency distribution

Many techniques are used for the formation of the group frequency distribution. For group of observations, we divide the data into class intervals and difference between upper and lower interval is called the width of the class interval. There are few points that must be kept in mind while preparing a group frequency table.

(a) C lass type : One should define class type in a very clear manner. It should be exhaustive and mutualy exclusive so that variableâs value must be assigned to only one class in the table.

(b)Â Class Intervals: It means how many intervals should be formed for the available data. Number of intervals depend on the things like number of observations in the data, its magnitude value, level of precision and further analysis of the data.

The most common formula that is used for the determination of the interval in the group frequency distribution is Sturgeâs rule:

k= 1 + 3.322 log 10 N

where is the number of classes and N is the total number of observations in the data. This rule is used for correct determination of intervals in the data and it is further used for the determination of the width of the class interval.

(c) Width of class interval: Width of the interval means the difference between the lower limit and upper limit of the interval. The width of the interval is defined through the formula that is â = Range/No. of Classes

where â denote the width of the class interval and range is defined as the difference between the highest and lowest value of the data set.

(d)Â Class limits methods: There are different methods that are used for the classification of the data set on the basis of class interval. The limit consists of two numbers that are used for the purpose of tallying observations into various classes. There are two different methods for the classification of the data on the basis of class intervals. These are:- (a) Inclusive method and (b) Exclusive Method.

(i)Â Inclusive method: In inclusive method, the upper limit of a class interval is considered in the interval itself and is not related with the next class. For example, in inclusive method, the class limits are 0-4, 5-9, 10-14, 15-19 and so on. Hence one can see that both the upper and lower limits are included in the class and thus it is termed as inclusive. The main drawback of this method for continuous data observations for example if data value is 4.5 then with this method one cannot tabulate or assign the value to any interval.

(ii)Â Exclusive method: In this method, the data are classified into class interval of such time that upper limit of one interval is the lower limit of next succeeding class interval. For example, in exclusive method the class limits should be of such type that is 0-5, 5-10,10-15 and so on. Hence all those values that are less than 5 are considered in first interval andÂ all those data values that are above than 5 but less than 10 are counted in second interval.Â Hence in exclusive method, the problem of inclusive method is taken care of.

(e)Â Mid value or Mid points: Mid value is calculated by taking the sum of upper and lower limit of the interval and dividing that sum by 2. This value is used as a representative value of the class interval and it is used for evaluation of mean, median, mode and higher moments of the data.

Â Â In the next section, we will discuss about cumulative frequency distribution and how to construct it.

3.3 Cumulative Frequency Distribution

We have already discussed about the frequency distribution in the previous section. Frequency distribution counts the occurrence of the same value in the data but sometime one is interested in the number of observations that are small or greater than a given value. In such type of situation, one has to calculate the accumulated frequency less than or greater than some specified value. This accumulated value is known as Cumulative frequency distribution.

The frequency of observations till a given value is considered as less than cumulative frequency and the frequency of observations that are greater than a value is called more than cumulative frequency.

Using the same observation as given in Table No.4. The cumulative frequency distribution for both more and less than are given in the following table.

Table No. 5

From the above table, one can see the less than and more than cumulative frequency values of the data. These values are further used for graphical representation of the data. For example, ogive curve of more than and less than type use these values for plotting on the axis.

4.Â Use of Diagrammatic and Graphical Presentation of the Data

Diagrammatic and Graphical presentation of the data are useful in practice due to the following reasons.

(1)Â Â The information that we acquire from the graphical and diagrammatic representation of the data is easy to understand even for a layman person due to its simplicity.

(2)Â Â People are more interested in graphical presentation of facts then just numbers due to eye caching effect of diagram or pictures.

(3)Â Â Graphs and picture can simplify the complexity of the data that cannot be easily be understood with the figures.

(4)Â Â With the graphical presentation, one can easily compare the statistical data relating to different time and places to bring out the hidden facts and relationship among the statistical variables.

There are some limitations of diagrammatic and graphical representations like they do not show the details behind the numbers that can only be shown from the table in a better way. A single diagram or graph does not have a great importance rather than it is used for comparison purpose with other diagram or graph. In the next section, difference between graph and diagram will be discussed so that reader can understand the difference between them in a clear manner and use them at their proper place without any confusion.

4.1 Difference between diagrams and graphs

There are few rules based on them, one can differentiate between graphs and diagram but these rules are not standard for all so there is scope of changes in these rules among different persons. But we will discuss few rules that are considered common for all. These rules are:

(a)Â Â Diagram are plotted on the paper while graphs are plotted on a paper called graph paper graphs helps in the study of mathematical or numerical relationship between variables but in diagram precise relationship among variables are not discussed.

(b)Â Â In diagram , different tools like bars, rectangles, circles etc are used to present the information in the data. Whereas in graphs, different tools like lines, dots etc are used to present the data.

(c)Â Â Diagrams only give approximate information regarding the data as this information will not be used further for analysis purpose. On the other hand, graphs give more precise, accurate information about the data and they are used for further analysis purpose.

(d)Â Â Diagrams are used for the presentation of the categorical and geographical information in the data. On the other hand, graphs are used for the presentation of the time series and frequency distribution.

(e)Â Â Diagrams are more eye catching than graphs. Also diagrams are used for the understanding of the layman person but graphs are used by experts from the field for the further analysis of the information.

(f)Â Graphs are easier to build than comparative to the diagram.

There are few points based on which one keep in mind while constructing the diagrams. These are:-

- Diagram gives only a pictorial representation of the quantitative data for rough guesses;
- it can only be used for homogenous data;
- it is not reliable to make further inference about the data.

Â Â So, basically diagram are used for the graphical interpretation purpose only. One cannot use it to find out reasons or inference from the data.

While constructing diagrams, there are some general rules that should be followed. These are:-

- An appropriate diagram can only present the data in a better way. Thus, it is essential to choose the right diagram for the data that need expertise as well as knowledge. It may be possible that due to inappropriate selection of diagram the interpretation might be wrong that can lead to unbearable results.
- It is also important that a diagram should have an appropriate title corresponding to the nature of the data. With an appropriate title, a person can understand the main idea in the diagram.
- It should be constructed in such a way that it portray all the relevant information within an allotted space. So, it should be appropriate in terms of size and consistent in terms of dimensions.
- It should be neat, clean with footnotes and proper indexing that will attract the interest of the common man.

Â Â In the previous section, we discuss the characteristics of the appropriate diagram. Now in the following section, a brief note on different types of the diagrams will help to understand it importance.

4.2 Types of Diagrams

There are many types of diagram based on it dimensionality. These are

(i) One dimensional diagrams

(ii) Two dimensional diagrams

(iii) Pie Chart

(iv) Three dimensional diagrams

Each type of diagram is used for specific type of data i.e. for complex data, one need more dimensions to see the impact of one factor on the other. Hence the choice of the type of the data depends on the nature of the data. One dimensional diagram is discussed here to give elementary knowledge. One can read other dimensions diagram also from the references.

One dimensional diagrams

These types of diagram use only one dimension i.e. only length of bars and lines are taken into account. So, these diagrams are known as one-dimensional diagrams. Bars may be vertical or horizontal. Vertical bars are mostly used to represent growth or decline rate of the variable under study while horizontal bars are used to represent the data of attributes. There are few points that should be kept in mind while using bars.

(a) Bars should be constructed within an allotted space and of uniform shape and size. (b) Scale should be chosen according to the magnitude of the observations. (c) Bars must have the same base line for a given data. (d) It is better to represent the value at the top of the bar for the convenience of the reader. (e) Bars should be arranged from the left to right in order of magnitude for consistency.

The following example help you to understand the point given above.

The following data give the approximate average yield of rice in kg. per acre in different state of a country during a 2000-2001.

From the above figure, one can observe that the above diagram satisfies all the conditions. Hence one can easily understand the characteristics or facts of the data through diagrams in an easy manner.

Self- Checked Exercise

Question What are the benefits of using diagrammatic and graphical representation of the data?

Ans With the help of diagrammatic and graphical representation of the data even a layman person can understand the facts related with it. Although these techniques are not helpful to explain hidden factors influencing the variables or data.

Question How diagrammatic and graphical representation help in understanding the information contained in the data?

Ans As we are aware of the fact that one can understand the diagram or graphs in a better way than just numbers. Hence, one can easily understand the information contained in the data by using graphical and diagrammatical representations.

Question How graphical representation is different from diagrammatic presentation?

Ans In diagrammatic mode of presentation, one can use the devices like bars, rectangle etc whereas in graphical methods, one can use points, lines of different kind etc to present the information.

Data are collected from the resources of study and they are available in raw form. Thus after collecting and editing the data the next stage is to organize the data. Classification and tabulation of the data are among the most important tools for the precise, clear and comprehensible representation of the data. Frequency distribution and its various forms are discussed in the module. Graphical and diagrammatically forms and differences between them are discussed. Various forms of diagram one-diagram, two dimensional etc. are also used to represent the data in an understandable manner.

6. Suggested Readings

Agresti, A. and B. Finlay, Statistical Methods for the Social Science, 3rd Edition, Prentice Hall, 1997.

Daniel, W. W. and C. L. Cross, C. L., Biostatistics: A Foundation for Analysis in the Health Sciences, 10th Edition, John Wiley & Sons, 2013.

Hogg, R. V., J. Mckean and A. Craig, Introduction to Mathematical Statistics, Macmillan Pub. Co. Inc., 1978.

Meyer, P. L., Introductory Probability and Statistical Applications, Oxford & IBH Pub, 1975.

Triola, M. F., Elementary Statistics, 13th Edition, Pearson, 2017.

Weiss, N. A., Introductory Statistics, 10th Edition, Pearson, 2017.

y |

One can refer to the following links for further understanding of the statistics terms.

http://biostat.mc.vanderbilt.edu/wiki/pub/Main/ClinStat/glossary.pdf

http://www.stats.gla.ac.uk/steps/glossary/alphabet.html

http://www.reading.ac.uk/ssc/resources/Docs/Statistical_Glossary.pdf

https://stats.oecd.org/glossary/

http://www.statsoft.com/Textbook/Statistics-Glossary

https://www.stat.berkeley.edu/~stark/SticiGui/Text/gloss.htm

https://stats.oecd.org/glossary/alpha.asp?Let=A

## DIAGRAMMATIC REPRESENTATION OF DATA

An attractive representation of statistical data is provided by charts, diagrams and pictures.

Diagrammatic representation can be used for both the educated section and uneducated section of the society. Furthermore, any hidden trend present in the given data can be noticed only in this mode of representation.

However, compared to tabulation, this is less accurate.

So if there is a priority for accuracy, we have to recommend tabulation.

We are going to consider the following types of diagrams :

1. Line diagram

2. Histogram

3. Bar diagram

4. Pie chart

## Line Diagram

When the time series exhibit a wide range of fluctuations, we may think of logarithmic or ratio chart where "Log y" and not "y" is plotted against "t".

We use Multiple line chart for representing two or more related time series data expressed in the same unit and multiple â axis chart in somewhat similar situations, if the variables are expressed in different units.

The profits in thousand of dollars of an industrial house for 2002, 2003, 2004, 2005, 2006, 2007 and 2008 are 5, 8, 9, 6, 12, 15 and 24 respectively. Represent these data using a suitable diagram.

We can represent the profits for 7 consecutive years by drawing either a line diagram as given below.

Let us consider years on horizontal axis and profits on vertical axis.

For the year 2002, the profit is 5 thousand dollars. It can be written as a point (2002, 5)

In the same manner, we can write the following points for the succeeding years.

(2003, 8), (2004, 9), (2005, 6), (2006, 12), (2007, 15) and (2008, 24)

Now, plotting all these point and joining them using ruler, we can get the line diagram.

Showing line diagram for the profit of an Industrial House during 2002 to 2008.

A two dimensional graphical representation of a continuous frequency distribution is called a histogram.

In histogram, the bars are placed continuously side by side with no gap between adjacent bars.

That is, in histogram rectangles are erected on the class intervals of the distribution. The areas of rectangle are proportional to the frequencies.

Draw a histogram for the following table which represent the marks obtained by 100 students in an examination :

The class intervals are all equal with length of 10 marks.

Let us denote these class intervals along the X-axis.

Denote the number of students along the Y-axis, with appropriate scale.

The histogram is given below.

## Bar Diagram

There are two types of bar diagrams namely, Horizontal Bar diagram and Vertical bar diagram.

While horizontal bar diagram is used for qualitative data or data varying over space, the vertical bar diagram is associated with quantitative data or time series data.

Bars i.e. rectangles of equal width and usually of varying lengths are drawn either horizontally or vertically.

We consider Multiple or Grouped Bar diagrams to compare related series. Component or sub-divided Bar diagrams are applied for representing data divided into a number of components. Finally, we use Divided Bar charts or Percentage

Bar diagrams for comparing different components of a variable and also the relating of the components to the whole. For this situation, we may also use Pie chart or Pie diagram or circle diagram.

Example :

The total number of runs scored by a few players in one-day match is given.

Draw bar graph for the above data.

In a pie chart, the various observations or components are represented by the sectors of a circle and the whole circle represents the sum of the value of all the components .Clearly, the total angle of 360Â° at the center of the circle is divided according to the values of the components .

The central angle of a component is

= [Value of the component / Total value] x 360Â°

Sometimes, the value of the components are expressed in percentages. In such cases,

= [Percentage value of the component / 100] x 360Â°

The number of hours spent by a school student on various activities on a working day, is given below. Construct a pie chart using the angle measurement.

Draw a pie chart to represent the above information.

We may calculate the central angles for various components as follows :

From the above table, clearly, we obtain the required pie chart as shown below.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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## Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

- Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
- Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
- Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
- Line Plot – It shows the frequency of data on a given number line. â x â is placed above a number line each time when that data occurs again.
- Frequency Table – The table shows the number of pieces of data that falls within the given interval.
- Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
- Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
- Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

## General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

- Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
- Measurement Unit: Mention the measurement unit in the graph.
- Proper Scale: To represent the data in an accurate manner, choose a proper scale.
- Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
- Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
- Keep it Simple: Construct a graph in an easy way that everyone can understand.
- Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

## Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.Â There are two types of graphs to visually depict the information. They are:

- Time Series Graphs – Example: Line Graph
- Frequency Distribution Graphs – Example: Frequency Polygon Graph

## Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin âO’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

- Smoothed frequency graph
- Pie diagram
- Cumulative or ogive frequency graph
- Frequency Polygon

## Merits of Using Graphs

Some of the merits of using graphs are as follows:

- The graph is easily understood by everyone without any prior knowledge.
- It saves time
- It allows us to relate and compare the data for different time periods
- It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

## Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

- Obtain the frequency distribution and find the midpoints of each class interval.
- Represent the midpoints along x-axis and frequencies along the y-axis.
- Plot the points corresponding to the frequency at each midpoint.
- Join these points, using lines in order.
- To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | |

4 | 6 | 8 | 10 | 12 | 14 | 7 | 5 |

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

0-10 | 5 | 0 |

10-20 | 15 | 4 |

20-30 | 25 | 6 |

30-40 | 35 | 8 |

40-50 | 45 | 10 |

50-60 | 55 | 12 |

60-70 | 65 | 14 |

70-80 | 75 | 7 |

80-90 | 85 | 5 |

90-100 | 95 | 0 |

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

## Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

- Line Graphs
- Frequency Table
- Circle Graph, etc.

Read More:Â Types of Graphs

## What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

- It makes data more easily understandable.
- It saves time.
- It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

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## Ways To Improve Learning Outcomes: Learn Tips & Tricks

## The Three States of Matter: Solids, Liquids, and Gases

## Types of Motion: Introduction, Parameters, Examples

## Understanding Frequency Polygon: Detailed Explanation

## Uses of Silica Gel in Packaging?

## Visual Learning Style for Students: Pros and Cons

## Air Pollution: Know the Causes, Effects & More

## Sexual Reproduction in Flowering Plants

## Integers Introduction: Check Detailed Explanation

## Human Respiratory System – Detailed Explanation

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## Data Representation: Definition, Types, Examples

Data Representation: Data representation is a technique for analysing numerical data. The relationship between facts, ideas, information, and concepts is depicted in a diagram via data representation. It is a fundamental learning strategy that is simple and easy to understand. It is always determined by the data type in a specific domain. Graphical representations are available in many different shapes and sizes.

In mathematics, a graph is a chart in which statistical data is represented by curves or lines drawn across the coordinate point indicated on its surface. It aids in the investigation of a relationship between two variables by allowing one to evaluate the change in one variable’s amount in relation to another over time. It is useful for analysing series and frequency distributions in a given context. On this page, we will go through two different types of graphs that can be used to graphically display data. Continue reading to learn more.

## Data Representation in Maths

Definition: After collecting the data, the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data.

Any information gathered may be organised in a frequency distribution table, and then shown using pictographs or bar graphs. A bar graph is a representation of numbers made up of equally wide bars whose lengths are determined by the frequency and scale you choose.

The collected raw data can be placed in any one of the given ways:

- Serial order of alphabetical order
- Ascending order
- Descending order

## Data Representation Example

Example: Let the marks obtained by \(30\) students of class VIII in a class test, out of \(50\)according to their roll numbers, be:

\(39,\,25,\,5,\,33,\,19,\,21,\,12,41,\,12,\,21,\,19,\,1,\,10,\,8,\,12\)

\(17,\,19,\,17,\,17,\,41,\,40,\,12,41,\,33,\,19,\,21,\,33,\,5,\,1,\,21\)

The data in the given form is known as raw data or ungrouped data. The above-given data can be placed in the serial order as shown below:

Now, for say you want to analyse the standard of achievement of the students. If you arrange them in ascending or descending order, it will give you a better picture.

Ascending order:

\(1,\,1,\,5,\,5,\,8,\,10,\,12,12,\,12,\,12,\,17,\,17,\,17,\,19,\,19\)

\(19,\,19,\,21,\,21,\,21,\,25,\,33,33,\,33,\,39,\,40,\,41,\,41,\,41\)

Descending order:

\(41,\,41,\,41,\,40,\,39,\,33,\,33,33,\,25,\,21,\,21,\,21,\,21,\,19,\,19\)

\(19,\,19,\,17,\,17,\,17,\,12,\,12,12,\,12,\,10,\,8,\,5,\,5,1,\,1\)

When the raw data is placed in ascending or descending order of the magnitude is known as an array or arrayed data.

## Graph Representation in Data Structure

A few of the graphical representation of data is given below:

- Frequency distribution table

## Pictorial Representation of Data: Bar Chart

The bar graph represents the âqualitative data visually. The information is displayed horizontally or vertically and compares items like amounts, characteristics, times, and frequency.

The bars are arranged in order of frequency, so more critical categories are emphasised. By looking at all the bars, it is easy to tell which types in a set of data dominate the others. Bar graphs can be in many ways like single, stacked, or grouped.

## Graphical Representation of Data: Frequency Distribution Table

A frequency table or frequency distribution is a method to present raw data in which one can easily understand the information contained in the raw data.

The frequency distribution table is constructed by using the tally marks. Tally marks are a form of a numerical system with the vertical lines used for counting. The cross line is placed over the four lines to get a total of \(5\).

Consider a jar containing the different colours of pieces of bread as shown below:

Construct a frequency distribution table for the data mentioned above.

## Graphical Representation of Data: Histogram

The histogram is another kind of graph that uses bars in its display. The histogram is used for quantitative data, and ranges of values known as classes are listed at the bottom, and the types with greater frequencies have the taller bars.

A histogram and the bar graph look very similar; however, they are different because of the data level. Bar graphs measure the frequency of the categorical data. A categorical variable has two or more categories, such as gender or hair colour.

## Graphical Representation of Data: Pie Chart

The pie chart is used to represent the numerical proportions of a dataset. This graph involves dividing a circle into different sectors, where each of the sectors represents the proportion of a particular element as a whole. Thus, it is also known as a circle chart or circle graph.

## Graphical Representation of Data: Line Graph

A graph that uses points and lines to represent change over time is defined as a line graph. In other words, it is the chart that shows a line joining multiple points or a line that shows the link between the points.

The diagram illustrates the quantitative data between two changing variables with the straight line or the curve that joins a series of successive data points. Linear charts compare two variables on the vertical and the horizontal axis.

## General Rules for Visual Representation of Data

We have a few rules to present the information in the graphical representation effectively, and they are given below:

- Suitable Title: Ensure that the appropriate title is given to the graph, indicating the presentation’s subject.
- Measurement Unit: Introduce the measurement unit in the graph.
- Proper Scale: To represent the data accurately, choose an appropriate scale.
- Index: In the Index, the appropriate colours, shades, lines, design in the graphs are given for better understanding.
- Data Sources: At the bottom of the graph, include the source of information wherever necessary.
- Keep it Simple: Build the graph in a way that everyone should understand easily.
- Neat: You have to choose the correct size, fonts, colours etc., in such a way that the graph must be a model for the presentation of the information.

## Solved Examples on Data Representation

Q.1. Construct the frequency distribution table for the data on heights in \(({\rm{cm}})\) of \(20\) boys using the class intervals \(130 – 135,135 – 140\) and so on. The heights of the boys in \({\rm{cm}}\) are:

Ans: The frequency distribution for the above data can be constructed as follows:

Q.2. Write the steps of the construction of Bar graph? Ans: To construct the bar graph, follow the given steps: 1. Take a graph paper, draw two lines perpendicular to each other, and call them horizontal and vertical. 2. You have to mark the information given in the data like days, weeks, months, years, places, etc., at uniform gaps along the horizontal axis. 3. Then you have to choose the suitable scale to decide the heights of the rectangles or the bars and then mark the sizes on the vertical axis. 4. Draw the bars or rectangles of equal width and height marked in the previous step on the horizontal axis with equal spacing. The figure so obtained will be the bar graph representing the given numerical data.

Q.3. Read the bar graph and then answer the given questions: I. Write the information provided by the given bar graph. II. What is the order of change of the number of students over several years? III. In which year is the increase of the student maximum? IV. State whether true or false. The enrolment during \(1996 – 97\) is double that of \(1995 – 96\)

Ans: I. The bar graph represents the number of students in class \({\rm{VI}}\) of a school during the academic years \(1995 – 96\,to\,1999 – 2000\). II. The number of stcccccudents is changing in increasing order as the heights of bars are growing. III. The increase in the number of students in uniform and the increase in the height of bars is uniform. Hence, in this case, the growth is not maximum in any of the years. The enrolment in the years is \(1996 – 97\, = 200\). and the enrolment in the years is \(1995 – 96\, = 150\). IV. The enrolment in \(1995 – 97\,\) is not double the enrolment in \(1995 – 96\). So the statement is false.

Q.4. Write the frequency distribution for the given information of ages of \(25\) students of class VIII in a school. \(15,\,16,\,16,\,14,\,17,\,17,\,16,\,15,\,15,\,16,\,16,\,17,\,15\) \(16,\,16,\,14,\,16,\,15,\,14,\,15,\,16,\,16,\,15,\,14,\,15\) Ans: Frequency distribution of ages of \(25\) students:

Q.5. There are \(20\) students in a classroom. The teacher asked the students to talk about their favourite subjects. The results are listed below:

By looking at the above data, which is the most liked subject? Ans: Representing the above data in the frequency distribution table by using tally marks as follows:

From the above table, we can see that the maximum number of students \((7)\) likes mathematics.

Also, Check –

- Diagrammatic Representation of Data

In the given article, we have discussed the data representation with an example. Then we have talked about graphical representation like a bar graph, frequency table, pie chart, etc. later discussed the general rules for graphic representation. Finally, you can find solved examples along with a few FAQs. These will help you gain further clarity on this topic.

## FAQs on Data Representation

Q.1: How is data represented? A: The collected data can be expressed in various ways like bar graphs, pictographs, frequency tables, line graphs, pie charts and many more. It depends on the purpose of the data, and accordingly, the type of graph can be chosen.

Q.2: What are the different types of data representation? A : The few types of data representation are given below: 1. Frequency distribution table 2. Bar graph 3. Histogram 4. Line graph 5. Pie chart

Q.3: What is data representation, and why is it essential? A: After collecting the data, the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data. Importance: The data visualization gives us a clear understanding of what the information means by displaying it visually through maps or graphs. The data is more natural to the mind to comprehend and make it easier to rectify the trends outliners or trends within the large data sets.

Q.4: What is the difference between data and representation? A: The term data defines the collection of specific quantitative facts in their nature like the height, number of children etc., whereas the information in the form of data after being processed, arranged and then presented in the state which gives meaning to the data is data representation.

Q.5: Why do we use data representation? A: The data visualization gives us a clear understanding of what the information means by displaying it visually through maps or graphs. The data is more natural to the mind to comprehend and make it easier to rectify the trends outliners or trends within the large data sets.

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- School Guide
- Mathematics
- Number System and Arithmetic
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- Maths Formulas
- Class 8 Maths Notes
- Class 9 Maths Notes
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- Class 11 Maths Notes
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- CBSE Class 9 Maths Revision Notes

## Chapter 1: Number System

- Number System in Maths
- Natural Numbers | Definition, Examples & Properties
- Whole Numbers - Definition, Properties and Examples
- Rational Numbers: Definition, Examples, Worksheet
- Irrational Numbers: Definition, Examples, Symbol, Properties
- Real Numbers
- Decimal Expansion of Real Numbers
- Decimal Expansions of Rational Numbers
- Representation of Rational Numbers on the Number Line | Class 8 Maths
- Represent â3 on the number line
- Operations on Real Numbers
- Rationalization of Denominators
- Laws of Exponents for Real Numbers

## Chapter 2: Polynomials

- Polynomials in One Variable | Polynomials Class 9 Maths
- Polynomial Formula
- Types of Polynomials (Based on Terms and Degrees)
- Zeros of Polynomial
- Factorization of Polynomial
- Remainder Theorem
- Factor Theorem
- Algebraic Identities

## Chapter 3: Coordinate Geometry

- Coordinate Geometry
- Cartesian Coordinate System
- Cartesian Plane

## Chapter 4: Linear equations in two variables

- Linear Equations in One Variable
- Linear Equation in Two Variables
- Graph of Linear Equations in Two Variables
- Graphical Methods of Solving Pair of Linear Equations in Two Variables
- Equations of Lines Parallel to the x-axis and y-axis

## Chapter 5: Introduction to Euclid's Geometry

- Euclidean Geometry
- Equivalent Version of Euclidâs Fifth Postulate

## Chapter 6: Lines and Angles

- Lines and Angles
- Types of Angles
- Pairs of Angles - Lines & Angles
- Transversal Lines
- Angle Sum Property of a Triangle

## Chapter 7: Triangles

- Triangles in Geometry
- Congruence of Triangles |SSS, SAS, ASA, and RHS Rules
- Theorem - Angle opposite to equal sides of an isosceles triangle are equal | Class 9 Maths
- Triangle Inequality Theorem, Proof & Applications

## Chapter 8: Quadrilateral

- Angle Sum Property of a Quadrilateral
- Quadrilateral - Definition, Properties, Types, Formulas, Examples
- Introduction to Parallelogram: Properties, Types, and Theorem
- Rhombus: Definition, Properties, Formula and Examples
- Trapezium in Maths | Formulas, Properties & Examples
- Square in Maths - Area, Perimeter, Examples & Applications
- Kite - Quadrilaterals
- Properties of Parallelograms
- Mid Point Theorem

## Chapter 9: Areas of Parallelograms and Triangles

- Area of Triangle | Formula and Examples
- Area of Parallelogram | Definition, Formulas & Examples
- Figures on the Same Base and between the Same Parallels

## Chapter 10: Circles

- Circles in Maths
- Radius of Circle
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- What is the longest chord of a Circle?
- Circumference of Circle - Definition, Perimeter Formula, and Examples
- Angle subtended by an arc at the centre of a circle
- What is Cyclic Quadrilateral
- The sum of opposite angles of a cyclic quadrilateral is 180Â° | Class 9 Maths Theorem

## Chapter 11: Construction

- Basic Constructions - Angle Bisector, Perpendicular Bisector, Angle of 60Â°
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## Chapter 12: Heron's Formula

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## Chapter 13: Surface Areas and Volumes

- Surface Area of Cuboid
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## Chapter 14: Statistics

- Collection and Presentation of Data

Graphical Representation of Data

- Bar Graphs and Histograms
- Central Tendency in Statistics- Mean, Median, Mode
- Mean, Median and Mode

## Chapter 15: Probability

- Experimental Probability
- Empirical Probability
- CBSE Class 9 Maths Formulas
- NCERT Solutions for Class 9 Maths: Chapter Wise PDF 2024
- RD Sharma Class 9 Solutions

Graphical Representation of Data: Graphical Representation of Data,” where numbers and facts become lively pictures and colorful diagrams . Instead of staring at boring lists of numbers, we use fun charts, cool graphs, and interesting visuals to understand information better. In this exciting concept of data visualization, we’ll learn about different kinds of graphs, charts, and pictures that help us see patterns and stories hidden in data.

There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics .

The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, Astro statistics, and so on . In this article, we have provided everything about the graphical representation of data, including its types, rules, advantages, etc.

Table of Content

## What is Graphical Representation

Types of graphical representations, line graphs, histogramsÂ , stem and leaf plotÂ , box and whisker plotÂ .

- Graphical Representations used in Maths

## Value-Based or Time Series GraphsÂ

Frequency based, principles of graphical representations, advantages and disadvantages of using graphical system, general rules for graphical representation of data, frequency polygon, solved examples on graphical representation of data.

Graphics Representation is a way of representing any data in picturized form . It helps a reader to understand the large set of data very easily as it gives us various data patterns in visualized form.

There are two ways of representing data,

- Pictorial Representation through graphs.

They say, âA picture is worth a thousand wordsâ. Â It’s always better to represent data in a graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in the form of visuals as Human beings process data better in visual form than any other form.

Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time.

Check: Graph and its representations

Comparison between different items is best shown with graphs, it becomes easier to compare the crux of the data about different items. Let’s look at all the different types of graphical representations briefly:Â

A line graph is used to show how the value of a particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data and predicting further trends.Â

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars.Â

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range.Â

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point. Â

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4). Â

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data.Â

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole.Â

## Graphical Representations used in Math’s

Graphs in Math are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths:Â

- Value-Based or Time Series Graphs

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values.Â

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study.

Also read: Types of Statistical Data

- All types of graphical representations follow algebraic principles.
- When plotting a graph, there’s an origin and two axes.
- The x-axis is horizontal, and the y-axis is vertical.
- The axes divide the plane into four quadrants.
- The origin is where the axes intersect.
- Positive x-values are to the right of the origin; negative x-values are to the left.
- Positive y-values are above the x-axis; negative y-values are below.

- It gives us a summary of the data which is easier to look at and analyze.
- It saves time.
- We can compare and study more than one variable at a time.

## Disadvantages

- It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data.Â
- Interpretation of graphs can vary based on individual perspectives, leading to subjective conclusions.
- Poorly constructed or misleading visuals can distort data interpretation and lead to incorrect conclusions.

Check : Diagrammatic and Graphic Presentation of Data

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs:Â

- Whenever possible, the data source must be mentioned for the viewer.
- Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
- The measurement Unit should be mentioned in the top right corner of the graph.
- The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
- Last but not the least, a suitable title should be chosen.

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval.Â

Question 1: What are different types of frequency-based plots?Â

Types of frequency-based plots:Â Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels.Â

Draw a bar graph for the following data.Â

- Put each of the channels on the x-axis
- The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following dataÂ

- Put each of the x-axis row value on the x-axis
- joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data:Â

- Draw the class intervals on the x-axis and frequencies on the y-axis.
- Calculate the midpoint of each class interval.

Class Interval | Mid Point | Frequency |

0-3 | 1.5 | 3 |

3-6 | 4.5 | 4 |

6-9 | 7.5 | 2 |

9-12 | 10.5 | 6 |

Now join the mid points of the intervals and their corresponding frequencies on the graph.Â

This graph shows both the histogram and frequency polygon for the given distribution.

## Related Article:

Graphical Representation of Data| Practical Work in Geography Class 12 What are the different ways of Data Representation What are the different ways of Data Representation? Charts and Graphs for Data Visualization

## Conclusion of Graphical Representation

Graphical representation is a powerful tool for understanding data, but it’s essential to be aware of its limitations. While graphs and charts can make information easier to grasp, they can also be subjective, complex, and potentially misleading . By using graphical representations wisely and critically, we can extract valuable insights from data, empowering us to make informed decisions with confidence.

## Graphical Representation of Data – FAQs

What are the advantages of using graphs to represent data.

Graphs offer visualization, clarity, and easy comparison of data, aiding in outlier identification and predictive analysis.

## What are the common types of graphs used for data representation?

Common graph types include bar, line, pie, histogram, and scatter plots , each suited for different data representations and analysis purposes.

## How do you choose the most appropriate type of graph for your data?

Select a graph type based on data type, analysis objective, and audience familiarity to effectively convey information and insights.

## How do you create effective labels and titles for graphs?

Use descriptive titles, clear axis labels with units, and legends to ensure the graph communicates information clearly and concisely.

## How do you interpret graphs to extract meaningful insights from data?

Interpret graphs by examining trends, identifying outliers, comparing data across categories, and considering the broader context to draw meaningful insights and conclusions.

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## Advantages and Disadvantages of Diagrammatic Representation

Looking for advantages and disadvantages of Diagrammatic Representation?

We have collected some solid points that will help you understand the pros and cons of Diagrammatic Representation in detail.

But first, letâs understand the topic:

## What is Diagrammatic Representation?

What are the advantages and disadvantages of diagrammatic representation.

The following are the advantages and disadvantages of Diagrammatic Representation:

Advantages | Disadvantages |
---|---|

Visualizes complex data | Can oversimplify complex data |

Simplifies information interpretation | Misinterpretation risk |

Enhances memory retention | Requires graphical skills |

Facilitates quick comparison | Not detailed like text |

Engages audience effectively | Lacks depth for analysis |

## Advantages of Diagrammatic Representation

Disadvantages of diagrammatic representation.

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## Data Visualization

Table of contents, what is data visualization, importance of data visualization in cybersecurity, types of data visualization in cybersecurity, benefits of data visualization, challenges of data visualization, best practices for effective data visualization in cybersecurity, how proofpoint uses data visualization.

In the realm of cybersecurity, data visualization is a highly useful tool, transforming complex data into comprehensible visual formats. This practice not only supports the swift detection of threats but also enhances the overall decision-making process among cybersecurity and IT teams who oversee an organizationâs infrastructure. By converting raw data into visual narratives, professionals can better understand and respond to potential vulnerabilities and attacks.

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Data visualization is the process of converting elaborate datasets into visual contexts, such as charts, graphs, or maps, to make complex information more accessible and comprehensible for the human brain to interpret. This exercise simplifies the interpretation of data and distills patterns, anomalies, and trends that are less detectable by viewing source data at large.

The primary purpose of data visualization is multifaceted: it simplifies complex data, enhances decision-making processes, and improves communication between technical and non-technical stakeholders. By converting vast amounts of information into visual formats, data visualization enables quicker and more informed decision-making, as stakeholders can easily grasp the implications of data trends and anomalies.

This leads to more effective strategies and responses, particularly crucial in fields like cybersecurity , where data can be intricate and voluminous. The transformation process involves several key steps, including data collection and preprocessing, defining visualization goals, creating visual representations, analysis and interpretation, and sharing results for collaboration.

In cybersecurity, data visualization is critical in threat detection and monitoring, mitigation and response to attacks, and analytics and reporting. It enables security teams to quickly identify patterns and anomalies indicating potential threats, provide real-time insights during an attack, and analyze large volumes of security data to inform future security measures.

Data visualization plays a crucial role in cybersecurity by transforming complex security data into easily digestible visual formats. With this transformation, security professionals can quickly identify patterns, anomalies, and potential threats that might otherwise go unnoticed in raw data.

In threat detection, data visualization helps analysts spot unusual patterns or behaviors that could indicate a data breach . For instance, a heat map of network traffic can instantly highlight areas of unusually high activity, potentially signaling a DDoS attack . Similarly, visualizing user login attempts across different time zones can reveal suspicious access patterns that might suggest credential theft.

During incident response, visualization tools provide real-time insights into the nature and scope of an ongoing attack. A dynamic network graph, for example, can show the spread of malware through a system, allowing responders to quickly isolate affected nodes and prevent further propagation. This visual representation of the attackâs progression enables faster and more effective containment strategies.

In security monitoring, data visualization aids in continuously assessing an organizationâs security posture. Dashboard visualizations can present key security metrics at a glance, such as the number of blocked intrusion attempts, system vulnerabilities, or compliance status. These visual summaries allow security teams to maintain situational awareness and prioritize their efforts effectively.

Several scenarios demonstrate the critical importance of data visualization in cybersecurity:

- Identifying patterns in security logs : By visualizing log data as timelines or charts, analysts can quickly spot trends or anomalies that might indicate a security issue. For example, a sudden spike in failed login attempts across multiple accounts could be visualized as a clear peak on a graph, alerting analysts to a potential brute-force attack .
- Visualizing network traffic : Network flow visualizations can reveal communication patterns between devices, helping identify unauthorized connections or data exfiltration attempts. A chord diagram, for instance, can effectively illustrate the volume and direction of traffic between different network segments, making it easier to spot unusual data flows.
- Mapping attack surfaces : Visualizing an organizationâs digital assets and their interconnections can help map attack surfaces and identify potential vulnerabilities. A tree map or network diagram can illustrate the relationships between systems, highlighting critical nodes that might require additional protection.
- Analyzing malware behavior : Visual representations of malware behavior, such as process trees or file system changes, can help analysts understand the impact and spread of malicious software more quickly than by reviewing raw log files.
- Tracking threat intelligence : Geospatial visualizations can map the origin of cyber threats globally, helping organizations understand the geographic distribution of attacks to adjust their defenses accordingly.

By leveraging data visualization techniques, cybersecurity professionals can better detect, respond to, and mitigate security threats more efficiently. This visual approach not only improves the speed and accuracy of threat analysis but also facilitates better communication of complex security concepts to non-technical stakeholders, ultimately strengthening an organizationâs overall security posture.

Several types of data visualization are commonly used in cybersecurity to represent complex data and facilitate quick insights. Here are some of the most prevalent:

- Network graphs : These visualizations depict connections between different nodes in a network, helping to identify unusual patterns or potential cyber-attack paths. Theyâre particularly useful for understanding the spread of malware or mapping data exfiltration routes.
- Heat maps : Heat maps use color-coding to represent data intensity, making them ideal for visualizing large datasets. In cybersecurity, they can highlight areas of high network activity or frequent security incidents.
- Time series charts : These charts show data points over time to indicate trends and anomalies. Theyâre often used to visualize network traffic patterns or the frequency of security events.
- Treemaps : Treemaps display hierarchical data as nested rectangles. Each rectangleâs size corresponds to the data pointâs relative importance. Theyâre useful for visualizing complex system structures or resource allocation.
- Scatter plots : These plots show the relationship between two variables and can help identify outliers. In cybersecurity, they might be used to correlate different types of security events or analyze user behavior.
- Pie charts and bar graphs : While simple, these classic visualizations can effectively show proportions and comparisons, such as the distribution of different types of security incidents.
- Geospatial maps : These visualizations plot data on geographic maps, helping to identify the origin of attacks or visualize the global distribution of threats.
- Sankey diagrams : These diagrams illustrate the flow of data or resources through a system, making them useful for visualizing data movement or attack progression.

Data visualization offers numerous advantages in the context of cybersecurity:

- Rapid threat detection : Visual representations allow analysts to quickly identify anomalies and potential threats that might be missed in raw data.
- Improved pattern recognition : Visualizations make spotting trends and patterns in large datasets easier, enhancing threat intelligence capabilities.
- Enhanced decision-making : By presenting complex data in an easily digestible format, visualizations support faster and more informed decision-making during incident response .
- Increased situational awareness : Real-time visualizations provide a comprehensive view of an organizationâs security posture, allowing for proactive threat management.
- Better communication : Visual representation helps bridge the gap between technical and non-technical stakeholders, facilitating clearer communication of security concepts and risks.
- Time efficiency : Visualizations can save considerable time in data analysis, allowing security teams to focus on addressing threats rather than sifting through raw data.
- Predictive analysis : By visualizing historical data and trends, security teams can better predict and prepare for future threats.
- Simplified compliance reporting : Visualizations can streamline the process of demonstrating compliance with various security standards and regulations.
- Improved incident response : During an attack, visualizations can provide real-time insights into the nature and scope of the threat, enabling more effective response strategies.
- Enhanced training and education : Visual representations of security concepts and scenarios can be powerful tools for training new security personnel and employees about security risks .

By leveraging these benefits, organizations can significantly enhance their cybersecurity posture, making it easier to detect, respond to, and mitigate threats in an increasingly complex digital landscape.

While data visualization offers numerous benefits in cybersecurity, organizations often face several challenges when implementing and utilizing these tools:

- Data overload : The sheer volume of cybersecurity data can be overwhelming. Organizations struggle to determine which data points are most relevant and how to visualize them without creating cluttered, confusing displays.
- Real-time processing : Cybersecurity requires real-time insights, but processing and visualizing large amounts of data in real-time can be technically challenging and resource-intensive.
- Data integration : Organizations often use multiple security tools, each generating its own data. Integrating these diverse data sources into cohesive visualizations can be complex and time-consuming.
- Skill gap : Effective data visualization requires a combination of technical skills, design knowledge, and cybersecurity expertise. Many organizations lack personnel with this diverse skill set.
- Scalability : As networks grow and threats evolve, visualization tools must scale accordingly. Ensuring that visualizations remain effective and performant as data volumes increase is a significant challenge.
- Context preservation : Simplifying data must be balanced with the risk of oversimplification. Maintaining the necessary context and nuance in visualizations without overwhelming users is key.
- User adoption : Introducing new visualization tools often elicits resistance from users accustomed to traditional methods. Overcoming this resistance and ensuring widespread adoption can be challenging.
- Privacy and security concerns : Visualizations may inadvertently reveal sensitive information. Ensuring that visualizations provide insights without compromising data security is a constant concern.

Addressing these challenges requires a methodical approach that employs proper planning, tech utilization, and best practices.

To maximize the benefits of data visualization in cybersecurity, organizations should adhere to the following best practices:

- Clarity and simplicity : Keep visualizations clear and straightforward. Avoid cluttering displays with unnecessary information. Each visualization should have a specific purpose and convey its message.
- Accuracy : Visuals should accurately present the underlying data in a way that makes logical sense for interpretation. Misleading visualizations can lead to poor decision-making and potentially compromise security.
- Consistency : Use consistent color schemes, shapes, and layouts across different visualizations. This helps users quickly understand and interpret various displays.
- Interactivity : Implement interactive features allowing users to drill down into data, filter information, and customize views based on their needs.
- Context-awareness : Provide necessary context alongside visualizations. This information might include time frames, data sources, or relevant benchmarks to help users interpret the data correctly.
- Real-time updates : In cybersecurity, timely information is crucial. Ensure visualizations update in real-time or near-real-time to provide the most current insights.
- User-centric design : Consider user needs and preferences when designing visualizations. Different roles may require different types of visualizations or levels of detail.
- Integration : Ensure visualization tools integrate seamlessly with existing security infrastructure and workflows to maximize adoption and effectiveness.
- Continuous improvement : Regularly gather feedback from users and iterate on your visualizations. As threats evolve and user needs change, your visualization strategies should adapt accordingly.

By following these best practices, organizations can significantly bolster their cybersecurity measures through effective data visualization. Remember, the goal is to transform complex data into actionable insights that enable faster, more informed decision-making in the face of evolving cyber threats.

Proofpoint leverages data visualization across its cybersecurity solutions to enhance threat detection, streamline investigations, and improve overall security posture. Here are some ways Proofpoint incorporates data visualization:

- eDiscovery and Compliance : Proofpoint Discover offers advanced visualization tools for eDiscovery processes. It provides conversation threading, interaction analysis, and timeline graphing to help users understand communication patterns and key custodians. The Case Management dashboard offers a comprehensive view of eDiscovery workflows, allowing users to track case activities and organize searches, holds, and exports.
- Threat Detection : Proofpoint uses heat maps and excess exposure charts to indicate areas where organizations are most vulnerable to data loss and compliance risks. These visualizations help quickly identify anomalies and potential threats that might be missed in raw data.
- Data Loss Prevention (DLP) : Proofpointâs DLP solutions use visualization to help organizations understand where sensitive data resides and who has access to it. Heat maps and charts provide insights into data exposure and help prioritize remediation efforts.
- User and Entity Behavior Analytics (UEBA) : Proofpoint employs behavioral AI and visualization techniques to detect anomalies that may indicate risky activities or insider threats via UEBA tools. These visualizations provide early warnings and help prevent data leaks or breaches.
- Compliance Monitoring : Proofpointâs compliance solutions use AI-based visualization to detect misconduct across various communication platforms. These tools help unify, manage, and investigate digital communications for corporate and regulatory compliance .

By integrating these visualization capabilities across its product suite, Proofpoint enables organizations to quickly identify risks, streamline investigations, and make data-driven decisions to reinforce their cybersecurity posture. The emphasis on visual representation of complex data sets allows for faster insights and more effective threat mitigation strategies. To learn more, contact Proofpoint .

## Related Resources

3 ways that good data visualization helps uncover e-discovery insights, interactive data visualization: how to identify authorized senders in a sea of sending ips, identity threat detection and response: challenges and solutions, proofpoint recognized in 2023 gartnerÂź market guide for data loss preventionÂ , subscribe to the proofpoint blog, ready to give proofpoint a try.

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Summary of Chemical Representations:

Chemical representations encompass various methods to model molecules, reactions, and macromolecules. Structural keys like MACCS and CATS encode the presence of specific chemical groups. Hashed fingerprints like Daylight and ECFP use hash functions to represent molecular patterns. Reactions are described using formats like Reaction SMILES, RInChI, and CGR. Macromolecules, including proteins and peptides, utilize sequence-based notations and structures from repositories like the PDB. These diverse methods facilitate accurate analysis and prediction in chemical informatics and drug discovery.

Graphical Representations for Molecules and Macromolecules:

Graphical representations of molecules, crucial for visualization and analysis, include 2D depictions and 3D models. 2D depictions show skeletal structures, often using standardized IUPAC guidelines, but still face challenges in layout and rendering. Tools like RDKit and CDK have improved 2D visualizations. For macromolecules, depictions focus on polymer or peptide structures, with tools like the Pfizer Macromolecule Editor aiding visualization. 3D depictions, using software such as Avogadro and PyMOL, include ball-and-stick, cartoon, and van der Waals models, facilitating studies in docking, protein-ligand interactions, and mechanistic studies. These representations enhance understanding of cheminformatics and drug discovery.

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## Sana Hassan

Sana Hassan, a consulting intern at Marktechpost and dual-degree student at IIT Madras, is passionate about applying technology and AI to address real-world challenges. With a keen interest in solving practical problems, he brings a fresh perspective to the intersection of AI and real-life solutions.

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## COMMENTS

A diagram is a visual snapshot of information. Think of diagrams as visual representations of data or information that communicate a concept, idea, or process in a simplified and easily understandable way. You can also use them to illustrate relationships, hierarchies, cycles, or workflows.

Diagrammatic representations improve the overall representation of data to a large extent. As the data is classified into several groups and presented in a systematic manner in diagrams, the whole presentation of data gets improved during the diagrammatic representation.

Representation of any numerical data by using diagrams is known as diagrammatic representation. Diagrammatic data representations give a simple and easy understanding of any numerical data collected as compared with the tabular form of the data or textual form of the data.

The tabular data is difficult to understand for a layman. However, a single glance at the diagram provides a thorough picture of the presented data. Thus, the diagrammatic representation method is simple and easy to understand.

Diagrammatic and graphic presentation of data means visual representation of the data. It shows a comparison between two or more sets of data and helps in the presentation of highly complex data in its simplest form.

Besides the tabular form, the data may also be presented in some graphic or diagrammatic form. "The transformation of data through visual methods like graphs, diagrams, maps and charts is called representation of data."

Bar Diagram. This is one of the simplest techniques to do the comparison for a given set of data. A bar graph is a graphical representation of the data in the form of rectangular bars or columns of equal width. It is the simplest one and easily understandable among the graphs by a group of people.

The diagrammatic presentation of data gives an immediate understanding of the real situation to be defined by the data in comparison to the tabular presentation of data or textual representations. It translates the highly complex ideas included in numbers into a more concrete and quickly understandable form pretty effectively.

Diagrams play an important role in statistical data presentation. Diagrams are nothing but geometrical figures like lines, bars, circles, squares, etc. Diagrammatic data presentation allows us to understand the data in an easier manner.

Nowadays a lot of emphases is laid upon exceptional presentation of data. All of this is because, when presented diagrammatically, data is easy to interpret with just a glance. In such a case we need to learn how to represent data diagrammatically via bar diagrams, pie charts etc.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

A diagrammatic representation of data is defined as a representation of data aided by diagrams to boost the simplicity of the statistics surrounding the concerned data. These diagrams are just geometrical figures used to enhance the overall presentation and provide visual aid to the reader.

Representation of data assisted by diagrams to increase the simplicity of the statistics surrounding the concerned data is defined as a diagrammatic representation of data. These diagrams are nothing but the use of geometrical figures to improve the overall presentation and offer visual assistance for the reader.

Diagrammatic representation refers to the process of representing numerical data of any kind through the use of diagrams.

The diagrammatic representation of data is a method used in the analysis and exploration of information with the help of diagrams. It refers to different methods that convert numbers into graphic forms, such as bar graphs, circle charts, and histograms. This also includes the use of color, layout, and shape to encode data.

In this module, a complete explanation about different types of diagrammatic representation of data will be discussed. This module helps one to learn different methods of diagrammatic presentation and their properties. Through this module, one can learn about which method of representation is appropriate under what type of conditions. Questions with answers are included to give an in-depth ...

Diagrammatic representation can be used for both the educated section and uneducated section of the society. Furthermore, any hidden trend present in the given data can be noticed only in this mode of representation. However, compared to tabulation, this is less accurate. So if there is a priority for accuracy, we have to recommend tabulation.

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical ...

Data Representation: Data representation is a technique for analysing numerical data. The relationship between facts, ideas, information, and concepts is depicted in a diagram via data representation. It is a fundamental learning strategy that is simple and easy to understand. It is always determined by the data type in a specific domain.

Graphical Representation of Data: Graphical Representation of Data," where numbers and facts become lively pictures and colorful diagrams. Instead of staring at boring lists of numbers, we use fun charts, cool graphs, and interesting visuals to understand information better. In this exciting concept of data visualization, we'll learn about different kinds of graphs, charts, and pictures ...

In this chapter you will learn how to: display numerical data in stem-and-leaf diagrams, histograms and cumulative frequency graphs interpret statistical data presented in various forms select an appropriate method for displaying data. PREREQUISITE KNOWLEDGE

A diagrammatic representation is a simple drawing that uses shapes, lines, and pictures to show information or explain an idea clearly.

Discover the importance of data visualization in cybersecurity, its key techniques, tools, and best practices to enhance threat detection and security monitoring.

Diagrammatic representation of the data section provides a high-level overview of the data in a report. It provides a context for the data and helps the reader understand how it was analysed. This section also includes any relevant background information to help the reader understand the data presented in the rest of the report.

Multiple representations have been proven to be an effective way of problem resolution in mechanics, a critical area of research in engineering. Multiple representations relate to the use of multiple modes of representation to express the same problem or notion, such as graphs, diagrams, equations, and words.

Advances in Chemical Representations and AI in Drug Discovery: The past century's technological advancements, especially the computer revolution and high-throughput screening in drug discovery, have necessitated the development of molecular representations readable by computers and understandable across scientific disciplines. Initially, molecules were depicted as structure diagrams with bonds ...