essay for statistics

There are lies, damned lies, and statistics. —Mark Twain

What this handout is about

The purpose of this handout is to help you use statistics to make your argument as effectively as possible.

Introduction

Numbers are power. Apparently freed of all the squishiness and ambiguity of words, numbers and statistics are powerful pieces of evidence that can effectively strengthen any argument. But statistics are not a panacea. As simple and straightforward as these little numbers promise to be, statistics, if not used carefully, can create more problems than they solve.

Many writers lack a firm grasp of the statistics they are using. The average reader does not know how to properly evaluate and interpret the statistics he or she reads. The main reason behind the poor use of statistics is a lack of understanding about what statistics can and cannot do. Many people think that statistics can speak for themselves. But numbers are as ambiguous as words and need just as much explanation.

In many ways, this problem is quite similar to that experienced with direct quotes. Too often, quotes are expected to do all the work and are treated as part of the argument, rather than a piece of evidence requiring interpretation (see our handout on how to quote .) But if you leave the interpretation up to the reader, who knows what sort of off-the-wall interpretations may result? The only way to avoid this danger is to supply the interpretation yourself.

But before we start writing statistics, let’s actually read a few.

Reading statistics

As stated before, numbers are powerful. This is one of the reasons why statistics can be such persuasive pieces of evidence. However, this same power can also make numbers and statistics intimidating. That is, we too often accept them as gospel, without ever questioning their veracity or appropriateness. While this may seem like a positive trait when you plug them into your paper and pray for your reader to submit to their power, remember that before we are writers of statistics, we are readers. And to be effective readers means asking the hard questions. Below you will find a useful set of hard questions to ask of the numbers you find.

1. Does your evidence come from reliable sources?

This is an important question not only with statistics, but with any evidence you use in your papers. As we will see in this handout, there are many ways statistics can be played with and misrepresented in order to produce a desired outcome. Therefore, you want to take your statistics from reliable sources (for more information on finding reliable sources, please see our handout on evaluating print sources ). This is not to say that reliable sources are infallible, but only that they are probably less likely to use deceptive practices. With a credible source, you may not need to worry as much about the questions that follow. Still, remember that reading statistics is a bit like being in the middle of a war: trust no one; suspect everyone.

2. What is the data’s background?

Data and statistics do not just fall from heaven fully formed. They are always the product of research. Therefore, to understand the statistics, you should also know where they come from. For example, if the statistics come from a survey or poll, some questions to ask include:

• Who asked the questions in the survey/poll?
• What, exactly, were the questions?
• Who interpreted the data?
• What issue prompted the survey/poll?
• What (policy/procedure) potentially hinges on the results of the poll?
• Who stands to gain from particular interpretations of the data?

All these questions help you orient yourself toward possible biases or weaknesses in the data you are reading. The goal of this exercise is not to find “pure, objective” data but to make any biases explicit, in order to more accurately interpret the evidence.

3. Are all data reported?

In most cases, the answer to this question is easy: no, they aren’t. Therefore, a better way to think about this issue is to ask whether all data have been presented in context. But it is much more complicated when you consider the bigger issue, which is whether the text or source presents enough evidence for you to draw your own conclusion. A reliable source should not exclude data that contradicts or weakens the information presented.

An example can be found on the evening news. If you think about ice storms, which make life so difficult in the winter, you will certainly remember the newscasters warning people to stay off the roads because they are so treacherous. To verify this point, they tell you that the Highway Patrol has already reported 25 accidents during the day. Their intention is to scare you into staying home with this number. While this number sounds high, some studies have found that the number of accidents actually goes down on days with severe weather. Why is that? One possible explanation is that with fewer people on the road, even with the dangerous conditions, the number of accidents will be less than on an “average” day. The critical lesson here is that even when the general interpretation is “accurate,” the data may not actually be evidence for the particular interpretation. This means you have no way to verify if the interpretation is in fact correct.

There is generally a comparison implied in the use of statistics. How can you make a valid comparison without having all the facts? Good question. You may have to look to another source or sources to find all the data you need.

4. Have the data been interpreted correctly?

If the author gives you her statistics, it is always wise to interpret them yourself. That is, while it is useful to read and understand the author’s interpretation, it is merely that—an interpretation. It is not the final word on the matter. Furthermore, sometimes authors (including you, so be careful) can use perfectly good statistics and come up with perfectly bad interpretations. Here are two common mistakes to watch out for:

• Confusing correlation with causation. Just because two things vary together does not mean that one of them is causing the other. It could be nothing more than a coincidence, or both could be caused by a third factor. Such a relationship is called spurious.The classic example is a study that found that the more firefighters sent to put out a fire, the more damage the fire did. Yikes! I thought firefighters were supposed to make things better, not worse! But before we start shutting down fire stations, it might be useful to entertain alternative explanations. This seemingly contradictory finding can be easily explained by pointing to a third factor that causes both: the size of the fire. The lesson here? Correlation does not equal causation. So it is important not only to think about showing that two variables co-vary, but also about the causal mechanism.
• Ignoring the margin of error. When survey results are reported, they frequently include a margin of error. You might see this written as “a margin of error of plus or minus 5 percentage points.” What does this mean? The simple story is that surveys are normally generated from samples of a larger population, and thus they are never exact. There is always a confidence interval within which the general population is expected to fall. Thus, if I say that the number of UNC students who find it difficult to use statistics in their writing is 60%, plus or minus 4%, that means, assuming the normal confidence interval of 95%, that with 95% certainty we can say that the actual number is between 56% and 64%.

Why does this matter? Because if after introducing this handout to the students of UNC, a new poll finds that only 56%, plus or minus 3%, are having difficulty with statistics, I could go to the Writing Center director and ask for a raise, since I have made a significant contribution to the writing skills of the students on campus. However, she would no doubt point out that a) this may be a spurious relationship (see above) and b) the actual change is not significant because it falls within the margin of error for the original results. The lesson here? Margins of error matter, so you cannot just compare simple percentages.

Finally, you should keep in mind that the source you are actually looking at may not be the original source of your data. That is, if you find an essay that quotes a number of statistics in support of its argument, often the author of the essay is using someone else’s data. Thus, you need to consider not only your source, but the author’s sources as well.

Writing statistics

As you write with statistics, remember your own experience as a reader of statistics. Don’t forget how frustrated you were when you came across unclear statistics and how thankful you were to read well-presented ones. It is a sign of respect to your reader to be as clear and straightforward as you can be with your numbers. Nobody likes to be played for a fool. Thus, even if you think that changing the numbers just a little bit will help your argument, do not give in to the temptation.

As you begin writing, keep the following in mind. First, your reader will want to know the answers to the same questions that we discussed above. Second, you want to present your statistics in a clear, unambiguous manner. Below you will find a list of some common pitfalls in the world of statistics, along with suggestions for avoiding them.

1. The mistake of the “average” writer

Nobody wants to be average. Moreover, nobody wants to just see the word “average” in a piece of writing. Why? Because nobody knows exactly what it means. There are not one, not two, but three different definitions of “average” in statistics, and when you use the word, your reader has only a 33.3% chance of guessing correctly which one you mean.

For the following definitions, please refer to this set of numbers: 5, 5, 5, 8, 12, 14, 21, 33, 38

• Mean (arithmetic mean) This may be the most average definition of average (whatever that means). This is the weighted average—a total of all numbers included divided by the quantity of numbers represented. Thus the mean of the above set of numbers is 5+5+5+8+12+14+21+33+38, all divided by 9, which equals 15.644444444444 (Wow! That is a lot of numbers after the decimal—what do we do about that? Precision is a good thing, but too much of it is over the top; it does not necessarily make your argument any stronger. Consider the reasonable amount of precision based on your input and round accordingly. In this case, 15.6 should do the trick.)
• Median Depending on whether you have an odd or even set of numbers, the median is either a) the number midway through an odd set of numbers or b) a value halfway between the two middle numbers in an even set. For the above set (an odd set of 9 numbers), the median is 12. (5, 5, 5, 8 < 12 < 14, 21, 33, 38)
• Mode The mode is the number or value that occurs most frequently in a series. If, by some cruel twist of fate, two or more values occur with the same frequency, then you take the mean of the values. For our set, the mode would be 5, since it occurs 3 times, whereas all other numbers occur only once.

As you can see, the numbers can vary considerably, as can their significance. Therefore, the writer should always inform the reader which average he or she is using. Otherwise, confusion will inevitably ensue.

2. Match your facts with your questions

Be sure that your statistics actually apply to the point/argument you are making. If we return to our discussion of averages, depending on the question you are interesting in answering, you should use the proper statistics.

Perhaps an example would help illustrate this point. Your professor hands back the midterm. The grades are distributed as follows:

The professor felt that the test must have been too easy, because the average (median) grade was a 95.

When a colleague asked her about how the midterm grades came out, she answered, knowing that her classes were gaining a reputation for being “too easy,” that the average (mean) grade was an 80.

When your parents ask you how you can justify doing so poorly on the midterm, you answer, “Don’t worry about my 63. It is not as bad as it sounds. The average (mode) grade was a 58.”

I will leave it up to you to decide whether these choices are appropriate. Selecting the appropriate facts or statistics will help your argument immensely. Not only will they actually support your point, but they will not undermine the legitimacy of your position. Think about how your parents will react when they learn from the professor that the average (median) grade was 95! The best way to maintain precision is to specify which of the three forms of “average” you are using.

3. Show the entire picture

Sometimes, you may misrepresent your evidence by accident and misunderstanding. Other times, however, misrepresentation may be slightly less innocent. This can be seen most readily in visual aids. Do not shape and “massage” the representation so that it “best supports” your argument. This can be achieved by presenting charts/graphs in numerous different ways. Either the range can be shortened (to cut out data points which do not fit, e.g., starting a time series too late or ending it too soon), or the scale can be manipulated so that small changes look big and vice versa. Furthermore, do not fiddle with the proportions, either vertically or horizontally. The fact that USA Today seems to get away with these techniques does not make them OK for an academic argument.

Charts A, B, and C all use the same data points, but the stories they seem to be telling are quite different. Chart A shows a mild increase, followed by a slow decline. Chart B, on the other hand, reveals a steep jump, with a sharp drop-off immediately following. Conversely, Chart C seems to demonstrate that there was virtually no change over time. These variations are a product of changing the scale of the chart. One way to alleviate this problem is to supplement the chart by using the actual numbers in your text, in the spirit of full disclosure.

Another point of concern can be seen in Charts D and E. Both use the same data as charts A, B, and C for the years 1985-2000, but additional time points, using two hypothetical sets of data, have been added back to 1965. Given the different trends leading up to 1985, consider how the significance of recent events can change. In Chart D, the downward trend from 1990 to 2000 is going against a long-term upward trend, whereas in Chart E, it is merely the continuation of a larger downward trend after a brief upward turn.

One of the difficulties with visual aids is that there is no hard and fast rule about how much to include and what to exclude. Judgment is always involved. In general, be sure to present your visual aids so that your readers can draw their own conclusions from the facts and verify your assertions. If what you have cut out could affect the reader’s interpretation of your data, then you might consider keeping it.

4. Give bases of all percentages

Because percentages are always derived from a specific base, they are meaningless until associated with a base. So even if I tell you that after this reading this handout, you will be 23% more persuasive as a writer, that is not a very meaningful assertion because you have no idea what it is based on—23% more persuasive than what?

Let’s look at crime rates to see how this works. Suppose we have two cities, Springfield and Shelbyville. In Springfield, the murder rate has gone up 75%, while in Shelbyville, the rate has only increased by 10%. Which city is having a bigger murder problem? Well, that’s obvious, right? It has to be Springfield. After all, 75% is bigger than 10%.

Hold on a second, because this is actually much less clear than it looks. In order to really know which city has a worse problem, we have to look at the actual numbers. If I told you that Springfield had 4 murders last year and 7 this year, and Shelbyville had 30 murders last year and 33 murders this year, would you change your answer? Maybe, since 33 murders are significantly more than 7. One would certainly feel safer in Springfield, right?

Not so fast, because we still do not have all the facts. We have to make the comparison between the two based on equivalent standards. To do that, we have to look at the per capita rate (often given in rates per 100,000 people per year). If Springfield has 700 residents while Shelbyville has 3.3 million, then Springfield has a murder rate of 1,000 per 100,000 people, and Shelbyville’s rate is merely 1 per 100,000. Gadzooks! The residents of Springfield are dropping like flies. I think I’ll stick with nice, safe Shelbyville, thank you very much.

Percentages are really no different from any other form of statistics: they gain their meaning only through their context. Consequently, percentages should be presented in context so that readers can draw their own conclusions as you emphasize facts important to your argument. Remember, if your statistics really do support your point, then you should have no fear of revealing the larger context that frames them.

Important questions to ask (and answer) about statistics

• Is the question being asked relevant?
• Do the data come from reliable sources?
• Margin of error/confidence interval—when is a change really a change?
• Are all data reported, or just the best/worst?
• Are the data presented in context?
• Have the data been interpreted correctly?
• Does the author confuse correlation with causation?

Now that you have learned the lessons of statistics, you have two options. Use this knowledge to manipulate your numbers to your advantage, or use this knowledge to better understand and use statistics to make accurate and fair arguments. The choice is yours. Nine out of ten writers, however, prefer the latter, and the other one later regrets his or her decision.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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How To Write a Statistical Analysis Essay

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Statistical analysis is a powerful tool used to draw meaningful insights from data. It can be applied to almost any field and has been used in everything from natural sciences, economics, and sociology to sports analytics and business decisions. Writing a statistical analysis essay requires an understanding of the concepts behind it as well as proficiency with data manipulation techniques.

In this guide, we’ll look at the steps involved in writing a statistical analysis essay. Experts in research paper writing from https://domypaper.me/write-my-research-paper/ give detailed instructions on how to properly conduct a statistical analysis and make valid conclusions.

Overview of statistical analysis essays

A statistical analysis essay is an academic paper that involves analyzing quantitative data and interpreting the results. It is often used in social sciences, economics and business to draw meaningful conclusions from the data. The objective of a statistical analysis essay is to analyze a specific dataset or multiple datasets in order to answer a question or prove or disprove a hypothesis. To achieve this effectively, the information must be analyzed using appropriate statistical techniques such as descriptive statistics, inferential statistics, regression analysis and correlation analysis.

Researching the subject matter

Before writing your statistical analysis essay it is important to research the subject matter thoroughly so that you have an understanding of what you are dealing with. This can include collecting and organizing any relevant data sets as well as researching different types of statistical techniques available for analyzing them. Furthermore, it is important to become familiar with the terminology associated with statistical analysis such as mean, median and mode.

Structuring your statistical analysis essay

The structure of your essay will depend on the type of data you are analyzing and the research question or hypothesis that you are attempting to answer. Generally speaking, it should include an introduction which introduces the research question or hypothesis; a body section which includes an overview of relevant literature; a description of how the data was collected and analyzed and any conclusions drawn from it; and finally a conclusion which summarizes all findings.

Analyzing data and drawing conclusions from it

After collecting and organizing your data, you must analyze it in order to draw meaningful conclusions from it. This involves using appropriate statistical techniques such as descriptive statistics, inferential statistics, regression analysis and correlation analysis. It is important to understand the assumptions made when using each technique in order to analyze the data correctly and draw accurate conclusions from it. When choosing a statistical technique for your research, it is important to consult with an expert https://typemyessay.me/service/research-paper-writing-service who can guide you on the most appropriate approach for your study.

Interpreting results and writing a conclusion

Once you have analyzed the data successfully, you must interpret the results carefully in order to answer your research question or prove/disprove your hypothesis. This involves making sure that any conclusions drawn are soundly based on the evidence presented. After interpreting the results, you should write a conclusion which summarizes all of your findings.

Using sources in your analysis

In order to back up your claims and provide support for your arguments, it is important to use credible sources within your analysis. This could include peer-reviewed articles, journals and books which can provide evidence to support your conclusion. It is also important to cite all sources used in order to avoid plagiarism.

Proofreading and finalizing your work

Once you have written your essay it is important to proofread it carefully before submitting it. This involves checking for grammar, spelling and punctuation errors as well as ensuring that the flow of the essay makes sense. Additionally, make sure that any references cited are correct and up-to-date. If you find it hard to complete your research statistical paper, you may want to consider buying a research paper for sale . This service can save you time and money, allowing you to focus on other important tasks.

Tips for writing a successful statistical analysis essay

Here are some tips for writing a successful statistical analysis essay:

• Research your subject matter thoroughly before writing your essay.
• Structure your paper according to the type of data you are analyzing.
• Analyze your data using appropriate statistical techniques.
• Interpret and draw meaningful conclusions from your results.
• Use credible sources to back up any claims or arguments made.
• Proofread and finalize your work before submitting it.

These tips will help ensure that your essay is well researched, structured correctly and contains accurate information. Following these tips will help you write a successful statistical analysis essay which can be used to answer research questions or prove/disprove hypotheses.

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Introductory essay

Written by the educators who created Visualizing Data, a brief look at the key facts, tough questions and big ideas in their field. Begin this TED Study with a fascinating read that gives context and clarity to the material.

The reality of today

All of us now are being blasted by information design. It's being poured into our eyes through the Web, and we're all visualizers now; we're all demanding a visual aspect to our information...And if you're navigating a dense information jungle, coming across a beautiful graphic or a lovely data visualization, it's a relief, it's like coming across a clearing in the jungle. David McCandless

In today's complex 'information jungle,' David McCandless observes that "Data is the new soil." McCandless, a data journalist and information designer, celebrates data as a ubiquitous resource providing a fertile and creative medium from which new ideas and understanding can grow. McCandless's inspiration, statistician Hans Rosling, builds on this idea in his own TEDTalk with his compelling image of flowers growing out of data/soil. These 'flowers' represent the many insights that can be gleaned from effective visualization of data.

We're just learning how to till this soil and make sense of the mountains of data constantly being generated. As Gary King, Director of Harvard's Institute for Quantitative Social Science says in his New York Times article "The Age of Big Data":

It's a revolution. We're really just getting under way. But the march of quantification, made possible by enormous new sources of data, will sweep through academia, business and government. There is no area that is going to be untouched.

How do we deal with all this data without getting information overload? How do we use data to gain real insight into the world? Finding ways to pull interesting information out of data can be very rewarding, both personally and professionally. The managing editor of Financial Times observed on CNN's Your Money : "The people who are able to in a sophisticated and practical way analyze that data are going to have terrific jobs." Those who learn how to present data in effective ways will be valuable in every field.

Many people, when they think of data, think of tables filled with numbers. But this long-held notion is eroding. Today, we're generating streams of data that are often too complex to be presented in a simple "table." In his TEDTalk, Blaise Aguera y Arcas explores images as data, while Deb Roy uses audio, video, and the text messages in social media as data.

Some may also think that only a few specialized professionals can draw insights from data. When we look at data in the right way, however, the results can be fun, insightful, even whimsical — and accessible to everyone! Who knew, for example, that there are more relationship break-ups on Monday than on any other day of the week, or that the most break-ups (at least those discussed on Facebook) occur in mid-December? David McCandless discovered this by analyzing thousands of Facebook status updates.

Data, data, everywhere

There is more data available to us now than we can possibly process. Every minute , Internet users add the following to the big data pool (i):

• 204,166,667 email messages sent
• More than 2,000,000 Google searches
• 684,478 pieces of content added on Facebook
• $272,070 spent by consumers via online shopping
• More than 100,000 tweets on Twitter
• 47,000 app downloads from Apple
• 34,722 "likes" on Facebook for different brands and organizations
• 27,778 new posts on Tumblr blogs
• 3,600 new photos on Instagram
• 3,125 new photos on Flickr
• 2,083 check-ins on Foursquare
• 571 new websites created
• 347 new blog posts published on Wordpress
• 217 new mobile web users
• 48 hours of new video on YouTube

These numbers are almost certainly higher now, as you read this. And this just describes a small piece of the data being generated and stored by humanity. We're all leaving data trails — not just on the Internet, but in everything we do. This includes reams of financial data (from credit cards, businesses, and Wall Street), demographic data on the world's populations, meteorological data on weather and the environment, retail sales data that records everything we buy, nutritional data on food and restaurants, sports data of all types, and so on.

Governments are using data to search for terrorist plots, retailers are using it to maximize marketing strategies, and health organizations are using it to track outbreaks of the flu. But did you ever think of collecting data on every minute of your child's life? That's precisely what Deb Roy did. He recorded 90,000 hours of video and 140,000 hours of audio during his son's first years. That's a lot of data! He and his colleagues are using the data to understand how children learn language, and they're now extending this work to analyze publicly available conversations on social media, allowing them to take "the real-time pulse of a nation."

Data can provide us with new and deeper insight into our world. It can help break stereotypes and build understanding. But the sheer quantity of data, even in just any one small area of interest, is overwhelming. How can we make sense of some of this data in an insightful way?

The power of visualizing data

Visualization can help transform these mountains of data into meaningful information. In his TEDTalk, David McCandless comments that the sense of sight has by far the fastest and biggest bandwidth of any of the five senses. Indeed, about 80% of the information we take in is by eye. Data that seems impenetrable can come alive if presented well in a picture, graph, or even a movie. Hans Rosling tells us that "Students get very excited — and policy-makers and the corporate sector — when they can see the data."

It makes sense that, if we can effectively display data visually, we can make it accessible and understandable to more people. Should we worry, however, that by condensing data into a graph, we are simplifying too much and losing some of the important features of the data? Let's look at a fascinating study conducted by researchers Emre Soyer and Robin Hogarth . The study was conducted on economists, who are certainly no strangers to statistical analysis. Three groups of economists were asked the same question concerning a dataset:

• One group was given the data and a standard statistical analysis of the data; 72% of these economists got the answer wrong.
• Another group was given the data, the statistical analysis, and a graph; still 61% of these economists got the answer wrong.
• A third group was given only the graph, and only 3% got the answer wrong.

Visualizing data can sometimes be less misleading than using the raw numbers and statistics!

What about all the rest of us, who may not be professional economists or statisticians? Nathalie Miebach finds that making art out of data allows people an alternative entry into science. She transforms mountains of weather data into tactile physical structures and musical scores, adding both touch and hearing to the sense of sight to build even greater understanding of data.

Another artist, Chris Jordan, is concerned about our ability to comprehend big numbers. As citizens of an ever-more connected global world, we have an increased need to get useable information from big data — big in terms of the volume of numbers as well as their size. Jordan's art is designed to help us process such numbers, especially numbers that relate to issues of addiction and waste. For example, Jordan notes that the United States has the largest percentage of its population in prison of any country on earth: 2.3 million people in prison in the United States in 2005 and the number continues to rise. Jordan uses art, in this case a super-sized image of 2.3 million prison jumpsuits, to help us see that number and to help us begin to process the societal implications of that single data value. Because our brains can't truly process such a large number, his artwork makes it real.

The role of technology in visualizing data

The TEDTalks in this collection depend to varying degrees on sophisticated technology to gather, store, process, and display data. Handling massive amounts of data (e.g., David McCandless tracking 10,000 changes in Facebook status, Blaise Aguera y Arcas synching thousands of online images of the Notre Dame Cathedral, or Deb Roy searching for individual words in 90,000 hours of video tape) requires cutting-edge computing tools that have been developed specifically to address the challenges of big data. The ability to manipulate color, size, location, motion, and sound to discover and display important features of data in a way that makes it readily accessible to ordinary humans is a challenging task that depends heavily on increasingly sophisticated technology.

The importance of good visualization

There are good ways and bad ways of presenting data. Many examples of outstanding presentations of data are shown in the TEDTalks. However, sometimes visualizations of data can be ineffective or downright misleading. For example, an inappropriate scale might make a relatively small difference look much more substantial than it should be, or an overly complicated display might obfuscate the main relationships in the data. Statistician Kaiser Fung's blog Junk Charts offers many examples of poor representations of data (and some good ones) with descriptions to help the reader understand what makes a graph effective or ineffective. For more examples of both good and bad representations of data, see data visualization architect Andy Kirk's blog at visualisingdata.com . Both consistently have very current examples from up-to-date sources and events.

Creativity, even artistic ability, helps us see data in new ways. Magic happens when interesting data meets effective design: when statistician meets designer (sometimes within the same person). We are fortunate to live in a time when interactive and animated graphs are becoming commonplace, and these tools can be incredibly powerful. Other times, simpler graphs might be more effective. The key is to present data in a way that is visually appealing while allowing the data to speak for itself.

Changing perceptions through data

While graphs and charts can lead to misunderstandings, there is ultimately "truth in numbers." As Steven Levitt and Stephen Dubner say in Freakonomics , "[T]eachers and criminals and real-estate agents may lie, and politicians, and even C.I.A. analysts. But numbers don't." Indeed, consideration of data can often be the easiest way to glean objective insights. Again from Freakonomics : "There is nothing like the sheer power of numbers to scrub away layers of confusion and contradiction."

Data can help us understand the world as it is, not as we believe it to be. As Hans Rosling demonstrates, it's often not ignorance but our preconceived ideas that get in the way of understanding the world as it is. Publicly-available statistics can reshape our world view: Rosling encourages us to "let the dataset change your mindset."

Chris Jordan's powerful images of waste and addiction make us face, rather than deny, the facts. It's easy to hear and then ignore that we use and discard 1 million plastic cups every 6 hours on airline flights alone. When we're confronted with his powerful image, we engage with that fact on an entirely different level (and may never see airline plastic cups in the same way again).

The ability to see data expands our perceptions of the world in ways that we're just beginning to understand. Computer simulations allow us to see how diseases spread, how forest fires might be contained, how terror networks communicate. We gain understanding of these things in ways that were unimaginable only a few decades ago. When Blaise Aguera y Arcas demonstrates Photosynth, we feel as if we're looking at the future. By linking together user-contributed digital images culled from all over the Internet, he creates navigable "immensely rich virtual models of every interesting part of the earth" created from the collective memory of all of us. Deb Roy does somewhat the same thing with language, pulling in publicly available social media feeds to analyze national and global conversation trends.

Roy sums it up with these powerful words: "What's emerging is an ability to see new social structures and dynamics that have previously not been seen. ...The implications here are profound, whether it's for science, for commerce, for government, or perhaps most of all, for us as individuals."

Let's begin with the TEDTalk from David McCandless, a self-described "data detective" who describes how to highlight hidden patterns in data through its artful representation.

David McCandless

The beauty of data visualization.

i. Data obtained June 2012 from “How Much Data Is Created Every Minute?” on http://mashable.com/2012/06/22/data-created-every-minute/ .

Relevant talks

Hans Rosling

The magic washing machine.

Nathalie Miebach

Art made of storms.

Chris Jordan

Turning powerful stats into art.

Blaise Agüera y Arcas

How photosynth can connect the world's images.

The birth of a word

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Writing with Descriptive Statistics

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This handout explains how to write with statistics including quick tips, writing descriptive statistics, writing inferential statistics, and using visuals with statistics.

Usually there is no good way to write a statistic. It rarely sounds good, and often interrupts the structure or flow of your writing. Oftentimes the best way to write descriptive statistics is to be direct. If you are citing several statistics about the same topic, it may be best to include them all in the same paragraph or section.

The mean of exam two is 77.7. The median is 75, and the mode is 79. Exam two had a standard deviation of 11.6.

Overall the company had another excellent year. We shipped 14.3 tons of fertilizer for the year, and averaged 1.7 tons of fertilizer during the summer months. This is an increase over last year, where we shipped only 13.1 tons of fertilizer, and averaged only 1.4 tons during the summer months. (Standard deviations were as followed: this summer .3 tons, last summer .4 tons).

Some fields prefer to put means and standard deviations in parentheses like this:

If you have lots of statistics to report, you should strongly consider presenting them in tables or some other visual form. You would then highlight statistics of interest in your text, but would not report all of the statistics. See the section on statistics and visuals for more details.

If you have a data set that you are using (such as all the scores from an exam) it would be unusual to include all of the scores in a paper or article. One of the reasons to use statistics is to condense large amounts of information into more manageable chunks; presenting your entire data set defeats this purpose.

At the bare minimum, if you are presenting statistics on a data set, it should include the mean and probably the standard deviation. This is the minimum information needed to get an idea of what the distribution of your data set might look like. How much additional information you include is entirely up to you. In general, don't include information if it is irrelevant to your argument or purpose. If you include statistics that many of your readers would not understand, consider adding the statistics in a footnote or appendix that explains it in more detail.

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• Inferential Statistics | An Easy Introduction & Examples

Inferential Statistics | An Easy Introduction & Examples

Published on September 4, 2020 by Pritha Bhandari . Revised on June 22, 2023.

While descriptive statistics summarize the characteristics of a data set, inferential statistics help you come to conclusions and make predictions based on your data.

When you have collected data from a sample , you can use inferential statistics to understand the larger population from which the sample is taken.

Inferential statistics have two main uses:

• making estimates about populations (for example, the mean SAT score of all 11th graders in the US).
• testing hypotheses to draw conclusions about populations (for example, the relationship between SAT scores and family income).

Table of contents

Descriptive versus inferential statistics, estimating population parameters from sample statistics, hypothesis testing, other interesting articles, frequently asked questions about inferential statistics.

Descriptive statistics allow you to describe a data set, while inferential statistics allow you to make inferences based on a data set.

• Descriptive statistics

Using descriptive statistics, you can report characteristics of your data:

• The distribution concerns the frequency of each value.
• The central tendency concerns the averages of the values.
• The variability concerns how spread out the values are.

In descriptive statistics, there is no uncertainty – the statistics precisely describe the data that you collected. If you collect data from an entire population, you can directly compare these descriptive statistics to those from other populations.

Inferential statistics

Most of the time, you can only acquire data from samples, because it is too difficult or expensive to collect data from the whole population that you’re interested in.

While descriptive statistics can only summarize a sample’s characteristics, inferential statistics use your sample to make reasonable guesses about the larger population.

With inferential statistics, it’s important to use random and unbiased sampling methods . If your sample isn’t representative of your population, then you can’t make valid statistical inferences or generalize .

Sampling error in inferential statistics

Since the size of a sample is always smaller than the size of the population, some of the population isn’t captured by sample data. This creates sampling error , which is the difference between the true population values (called parameters) and the measured sample values (called statistics).

Sampling error arises any time you use a sample, even if your sample is random and unbiased. For this reason, there is always some uncertainty in inferential statistics. However, using probability sampling methods reduces this uncertainty.

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The characteristics of samples and populations are described by numbers called statistics and parameters :

• A statistic is a measure that describes the sample (e.g., sample mean ).
• A parameter is a measure that describes the whole population (e.g., population mean).

Sampling error is the difference between a parameter and a corresponding statistic. Since in most cases you don’t know the real population parameter, you can use inferential statistics to estimate these parameters in a way that takes sampling error into account.

There are two important types of estimates you can make about the population: point estimates and interval estimates .

• A point estimate is a single value estimate of a parameter. For instance, a sample mean is a point estimate of a population mean.
• An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.

Both types of estimates are important for gathering a clear idea of where a parameter is likely to lie.

Confidence intervals

A confidence interval uses the variability around a statistic to come up with an interval estimate for a parameter. Confidence intervals are useful for estimating parameters because they take sampling error into account.

While a point estimate gives you a precise value for the parameter you are interested in, a confidence interval tells you the uncertainty of the point estimate. They are best used in combination with each other.

Each confidence interval is associated with a confidence level. A confidence level tells you the probability (in percentage) of the interval containing the parameter estimate if you repeat the study again.

A 95% confidence interval means that if you repeat your study with a new sample in exactly the same way 100 times, you can expect your estimate to lie within the specified range of values 95 times.

Although you can say that your estimate will lie within the interval a certain percentage of the time, you cannot say for sure that the actual population parameter will. That’s because you can’t know the true value of the population parameter without collecting data from the full population.

However, with random sampling and a suitable sample size, you can reasonably expect your confidence interval to contain the parameter a certain percentage of the time.

Your point estimate of the population mean paid vacation days is the sample mean of 19 paid vacation days.

Hypothesis testing is a formal process of statistical analysis using inferential statistics. The goal of hypothesis testing is to compare populations or assess relationships between variables using samples.

Hypotheses , or predictions, are tested using statistical tests . Statistical tests also estimate sampling errors so that valid inferences can be made.

Statistical tests can be parametric or non-parametric. Parametric tests are considered more statistically powerful because they are more likely to detect an effect if one exists.

Parametric tests make assumptions that include the following:

• the population that the sample comes from follows a normal distribution of scores
• the sample size is large enough to represent the population
• the variances , a measure of variability , of each group being compared are similar

When your data violates any of these assumptions, non-parametric tests are more suitable. Non-parametric tests are called “distribution-free tests” because they don’t assume anything about the distribution of the population data.

Statistical tests come in three forms: tests of comparison, correlation or regression.

Comparison tests

Comparison tests assess whether there are differences in means, medians or rankings of scores of two or more groups.

To decide which test suits your aim, consider whether your data meets the conditions necessary for parametric tests, the number of samples, and the levels of measurement of your variables.

Means can only be found for interval or ratio data , while medians and rankings are more appropriate measures for ordinal data .

Correlation tests

Correlation tests determine the extent to which two variables are associated.

Although Pearson’s r is the most statistically powerful test, Spearman’s r is appropriate for interval and ratio variables when the data doesn’t follow a normal distribution.

The chi square test of independence is the only test that can be used with nominal variables.

Regression tests

Regression tests demonstrate whether changes in predictor variables cause changes in an outcome variable. You can decide which regression test to use based on the number and types of variables you have as predictors and outcomes.

Most of the commonly used regression tests are parametric. If your data is not normally distributed, you can perform data transformations.

Data transformations help you make your data normally distributed using mathematical operations, like taking the square root of each value.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Confidence interval
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

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Descriptive statistics summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalizable to the broader population.

A statistic refers to measures about the sample , while a parameter refers to measures about the population .

A sampling error is the difference between a population parameter and a sample statistic .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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7.1: Basic Concepts of Statistics

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• Page ID 113176

• David Lippman & Jeff Eldridge
• Pierce College via The OpenTextBookStore

Learning Objectives

• Understand the basic terminology used in statistics
• Understand the difference between populations and samples
• Classify data as categorical or quantitative

Introduction

Like most people, you probably feel that it is important to "take control of your life." But what does this mean? Partly it means being able to properly evaluate the data and claims that bombard you every day. If you cannot distinguish good from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest. Statistics provides tools that you need in order to react intelligently to information you hear or read. In this sense, Statistics is one of the most important things that you can study.

To be more specific, here are some claims that we have heard on several occasions. (We are not saying that each one of these claims is true!)

• 4 out of 5 dentists recommend Dentyne.
• Almost 85% of lung cancers in men and 45% in women are tobacco-related.
• Condoms are effective 94% of the time.
• Native Americans are significantly more likely to be hit crossing the streets than are people of other ethnicities.
• People tend to be more persuasive when they look others directly in the eye and speak loudly and quickly.
• Women make 75 cents to every dollar a man makes when they work the same job.
• A surprising new study shows that eating egg whites can increase one's life span.
• People predict that it is very unlikely there will ever be another baseball player with a batting average over 400.
• There is an 80% chance that in a room full of 30 people that at least two people will share the same birthday.
• 79.48% of all statistics are made up on the spot.

All of these claims are statistical in character. We suspect that some of them sound familiar; if not, we bet that you have heard other claims like them. Notice how diverse the examples are; they come from psychology, health, law, sports, business, etc. Indeed, data and data-interpretation show up in discourse from virtually every facet of contemporary life.

Statistics are often presented in an effort to add credibility to an argument or advice. You can see this by paying attention to television advertisements. Many of the numbers thrown about in this way do not represent careful statistical analysis. They can be misleading, and push you into decisions that you might find cause to regret. For these reasons, learning about statistics is a long step towards taking control of your life. (It is not, of course, the only step needed for this purpose.) These chapters will help you learn statistical essentials. It will make you into an intelligent consumer of statistical claims.

You can take the first step right away. To be an intelligent consumer of statistics, your first reflex must be to question the statistics that you encounter. The British Prime Minister Benjamin Disraeli famously said, "There are three kinds of lies -- lies, damned lies, and statistics." This quote reminds us why it is so important to understand statistics. So let us invite you to reform your statistical habits from now on. No longer will you blindly accept numbers or findings. Instead, you will begin to think about the numbers, their sources, and most importantly, the procedures used to generate them.

We have put the emphasis on defending ourselves against fraudulent claims wrapped up as statistics. Just as important as detecting the deceptive use of statistics is the appreciation of the proper use of statistics. You must also learn to recognize statistical evidence that supports a stated conclusion. When a research team is testing a new treatment for a disease, statistics allows them to conclude based on a relatively small trial that there is good evidence their drug is effective. Statistics allowed prosecutors in the 1950’s and 60’s to demonstrate racial bias existed in jury panels. Statistics are all around you, sometimes used well, sometimes not. We must learn how to distinguish the two cases.

Basic Terms

In order to study and understand statistics, you must first be acquainted with the basic terminology.

Data are the individual items of information such as measurements or survey responses that have been collected for a study or analysis.

Statistics is a collection of methods for collecting, displaying, analyzing, and drawing conclusions from data.

There are 2 branches of statistics: descriptive and inferential.

Descriptive Statistics

Descriptive statistics is the branch of statistics that involves collecting, organizing, displaying, and describing data.

Inferential Statistics

Inferential statistics is the branch of statistics that uses probability to analyze, make predictions and draw conclusions based on the data.

We will mainly be exploring descriptive statistics in this class. To learn more about the methods of inferential statistics, you should take a course in introductory statistics.

Before we begin gathering and analyzing data we need to characterize the population we are studying. If we want to study the amount of money spent on textbooks by a typical first-year college student, our population might be all first-year students at your college. Or it might be:

• All first-year community college students in the state of California.
• All first-year students at public colleges and universities in the state of California.
• All first-year students at all colleges and universities in the state of California.
• All first-year students at all colleges and universities in the entire United States.

The population of a study is the group the collected data is intended to describe.

Sometimes the intended population is called the target population , since if we design our study badly, the collected data might not actually be representative of the intended population.

Why is it important to specify the population? We might get different answers to our question as we vary the population we are studying. First-year students at Cal State Fullerton might take slightly more diverse courses than those at your college, and some of these courses may require less popular textbooks that cost more; or, on the other hand, the University Bookstore might have a larger pool of used textbooks, reducing the cost of these books to the students. Whichever the case (and it is likely that some combination of these and other factors are in play), the data we gather from your college will probably not be the same as that from Cal State Fullerton. Particularly when conveying our results to others, we want to be clear about the population we are describing with our data.

Example \(\PageIndex{1}\)

A newspaper website contains a poll asking people their opinion on a recent news article. What is the population?

While the target (intended) population may have been all people, the real population of the survey is readers of the website.

If we were able to gather data on every member of our population, say the average (we will define "average" more carefully in a subsequent section) amount of money spent on textbooks by each first-year student at your college during the 2019-2020 academic year, the resulting number would be called a parameter .

A parameter is a value (average, percentage, etc.) calculated using all the data from a population.

We seldom see parameters, however, since surveying an entire population is usually very time-consuming and expensive, unless the population is very small or we already have the data collected.

A survey of an entire population is called a census .

You are probably familiar with two common censuses: the official government Census that attempts to count the population of the U.S. every ten years, and voting, which asks the opinion of all eligible voters in a district. The first of these demonstrates one additional problem with a census: the difficulty in finding and getting participation from everyone in a large population, which can bias, or skew, the results.

There are occasionally times when a census is appropriate, usually when the population is fairly small. For example, if the manager of Starbucks wanted to know the average number of hours her employees worked last week, she should be able to pull up payroll records or ask each employee directly.

Since surveying an entire population is often impractical, we usually select a sample to study.

A sample is a smaller subset of the entire population, ideally one that is fairly representative of the whole population.

We will discuss sampling methods in greater detail in a later section. For now, let us assume that samples are chosen in an appropriate manner. If we survey a sample, say 100 first-year students at your college, and find the average amount of money spent by these students on textbooks, the resulting number is called a statistic .

A statistic is a value (average, percentage, etc.) calculated using the data from a sample.

Example \(\PageIndex{2}\)

A researcher wanted to know how citizens of Brea felt about a voter initiative. To study this, she goes to the Brea Mall and randomly selects 200 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?

The sample is the 200 shoppers questioned. The population is less clear. While the intended population of this survey was Brea citizens, the effective population was mall shoppers. There is no reason to assume that the 200 shoppers questioned would be representative of all Brea citizens.

The 60% value was based on the sample, so it is a statistic.

Try It \(\PageIndex{1}\)

To determine the average length of trout in a lake, researchers catch 20 fish and measure them. What is the sample and population in this study?

The sample is the 20 fish caught. The population is all fish in the lake. The sample may be somewhat unrepresentative of the population since not all fish may be large enough to catch the bait.

Try It \(\PageIndex{2}\)

A college reports that the average age of their students is 28 years old. Is this a statistic or a parameter?

This is a parameter, since the college would have access to data on all students (the population).

Classifying Data

Once we have gathered data, we might wish to classify it. Roughly speaking, data can be classified as categorical data or quantitative data .

Categorical and Quantitative Data

• Categorical (qualitative) data are pieces of information that allow us to classify the objects under investigation into various categories. They are measurements for which there is no natural numerical scale, but which consist of attributes, labels, or other non-numerical characteristics.
• Quantitative data are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.

Example \(\PageIndex{3}\)

We might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater. Is the data collected categorical or quantitative?

When we conduct such a survey, the responses would look like: Top Gun: Maverick , Doctor Strange in the Multiverse of Madness , or Turning Red . We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like " Turning Red . " This would be categorical data.

Example \(\PageIndex{4}\)

A survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, ...). Is the data collected categorical or quantitative?

This would be quantitative data since the responses are numerical. We could perform meaningful arithmetic calculations on the data such as finding the average number of movies that people saw in a movie theater in the last year.

Other examples of quantitative data would be the running time of the movie you saw most recently (131 minutes, 126 minutes, 100 minutes, ...) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($10.50, $13.75, $16, ...).

Sometimes, determining whether or not data is categorical or quantitative can be a bit trickier.

Example \(\PageIndex{5}\)

Suppose we gather respondents' ZIP codes in a survey to track their geographical location. Is the data collected categorical or quantitative?

ZIP codes are numbers, but we can't do any meaningful mathematical calculations with them (it doesn't make sense to say that 92806 is "twice" 46403 — that's like saying that Anaheim, CA is "twice" Gary, IN, which doesn't make sense at all), so ZIP codes are really categorical data.

Example \(\PageIndex{6}\)

A survey about the movie you most recently attended includes the question "How would you rate the movie you just saw?" with these possible answers:

1 - It was awful 2 - It was just OK 3 - I liked it 4 - It was great 5 - Best movie ever!

Is the data collected categorical or quantitative?

Again, there are numbers associated with the responses, but we can't really do any calculations with them: a movie that rates a 4 is not necessarily twice as good as a movie that rates a 2, whatever that means; if two people see the movie and one of them thinks it stinks and the other thinks it's the best ever it doesn't necessarily make sense to say that "on average they liked it."

As we study movie-going habits and preferences, we shouldn't forget to specify the population under consideration. If we survey 3-7 year-olds the runaway favorite might be Turning Red . 13-17 year-olds might prefer Doctor Strange . And 33-37 year-olds might prefer Top Gun .

Try It \(\PageIndex{3}\)

Classify each measurement as categorical or quantitative:

• Eye color of a group of people
• Daily high temperature of a city over several weeks
• Annual income
• Categorical
• Quantitative

Statistics, Its Importance and Application Essay

Importance of statistics, examples of how statistics can be used.

Statistics is a science that helps businesses in decision-making. It entails the collection of data, tabulation, and inference making. In essence, Statistics is widely used in businesses to make forecasts, research on the market conditions, and ensure the quality of products. The importance of statistics is to determine the type of data required, how it is collected, and the way it is analyzed to get factual answers.

Statistics is the collection of numerical facts and figures on such things as population, education, economy, incomes, etc. Figures collected are referred to as data. The collection, analysis, and interpretation of data are referred to as statistical methods (Lind, Marchal, & Wathen, 2011).

Two subdivisions of the statistical method are:

• Descriptive statistics: Deals with compilation and presentation of data in various forms such as tables, graphs, and diagrams from which conclusions can be drawn and decisions made. Businesses, for example, use descriptive statistics when presenting their annual accounts and reports.
• Mathematical/inferential/inductive statistics: This deals with the tools of statistics. These are the techniques that are used to analyze, make estimates, inferences, and conclude the data collected (McClave, Benson, & Sincish, 2011).

Statistics have been collected since the earliest times in history. Rulers needed to have data on population and wealth so that taxes could be levied to maintain the state and the courts. Details on the composition of the population were necessary to determine the strength of the nation. With the growth of the population and the advent of the industrial revolution in the 18 th and 19 th centuries, there was a need for greater volumes of statistics in an increasing variety of subjects such as production, expenditure, incomes, imports, and exports. In the 19 th and 20 th centuries, governments worldwide took more control in economic activities such as education and health. This led to the enormous expansion of statistics collected by governments (Lind, Marchal, & Wathen, 2011).

The government’s economic activities have expanded in the last three centuries and so have the companies/businesses grown, as well. Indeed, some have grown to such an extent that their annual turnover is greater than the annual budgets of some governments. Big firms have to make decisions based on data. The companies collect data on their own other than these sources to establish:

• Competition
• Customer needs
• Production and personnel costs
• Accounting reports on liabilities, assets, losses, and income

The tools of statistics are important for companies in areas such as planning, forecasting, and quality control (McClave, Benson, & Sincish, 2011).

To Ensure Quality

A continuous check into quality using programs is very helpful in ensuring that only quality products come out of production firms. This, in turn, ensures that there is minimum wastage or errors in the production of goods and services (McClave, Benson, & Sincish, 2011).

Making Connections

Statistics are good in revealing relationships between variables – a good example is when a company makes a close relationship between the numbers of dissatisfied customers and the turnover. Indeed, there is an inverse relationship between the number of dissatisfied customers and turnover.

Backing Judgment

With only a small sample of the population studied, the management can come up with a concrete understanding of how the customers will relate to their products. This, therefore, will help them decide on whether to or not continue with that line of production (Lind, Marchal, & Wathen, 2011).

Lind, D., Marchal, G., & Wathen, A. (2011). Basic statistics for business and economics (7 th ed.). New York, NY: McGraw-Hill/Irwin.

McClave, T., Benson, G., & Sincish, T. (2011). Statistics for business and economics (11 th ed.). Boston, MA: Pearson-Prentice Hall.

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Essay on Statistics: Meaning and Definition of Statistics

“Statistics”, that a word is often used, has been derived from the Latin word ‘Status’ that means a group of numbers or figures; those represent some information of our human interest.

We find statistics in everyday life, such as in books or other information papers or TV or newspapers.

Although, in the beginning it was used by Kings only for collecting information about states and other information which was needed about their people, their number, revenue of the state etc.

This was known as the science of the state because it was used only by the Kings. So it got its development as ‘Kings’ subject or ‘Science of Kings’ or we may call it as “Political Arithmetic’s”. It was for the first time, perhaps in Egypt to conduct census of population in 3050 B.C. because the king needed money to erect pyramids. But in India, it is thought, that, it started dating back to Chandra Gupta Maurya’s kingdom under Chankya to collect the data of births and deaths. TM has also been stated in Chankya’s Arthshastra.

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But now-a-days due to its pervading nature, its scope has increased and widened. It is now used in almost in all the fields of human knowledge and skills like Business, Commerce, Economics, Social Sciences, Politics, Planning, Medicine and other sciences, Physical as well as Natural.

Definition :

The term ‘Statistics’ has been defined in two senses, i.e. in Singular and in Plural sense.

“Statistics has two meanings, as in plural sense and in singular sense”.

—Oxford Dictionary

In plural sense, it means a systematic collection of numerical facts and in singular sense; it is the science of collecting, classifying and using statistics.

A. In the Plural Sense :

“Statistics are numerical statements of facts in any department of enquiry placed in relation to each other.” —A.L. Bowley

“The classified facts respecting the condition of the people in a state—especially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.” —Webster

These definitions given above give a narrow meaning to the statistics as they do not indicate its various aspects as are witnessed in its practical applications. From the this point of view the definition given by Prof. Horace Sacrist appears to be the most comprehensive and meaningful:

“By statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose, and placed in relation to each other.”—Horace Sacrist

B. In the Singular Sense :

“Statistics refers to the body of technique or methodology, which has been developed for the collection, presentation and analysis of quantitative data and for the use of such data in decision making.” —Ncttor and Washerman

“Statistics may rightly be called the science of averages.” —Bowleg

“Statistics may be defined as the collection, presentation, analysis, and interpretation of numerical data.” —Croxton and Cowden

Stages of Investigations :

1. Collection of Data:

It is the first stage of investigation and is regarding collection of data. It is determined that which method of collection is needed in this problem and then data are collected.

2. Organisation of Data:

It is second stage. The data are simplified and made comparative and are classified according to time and place.

3. Presentation of Data:

In this third stage, organised data are made simple and attractive. These are presented in the form of tables diagrams and graphs.

4. Analysis of Data:

Forth stage of investigation is analysis. To get correct results, analysis is necessary. It is often undertaken using Measures of central tendencies, Measures of dispersion, correlation, regression and interpolation etc.

5. Interpretation of Data:

In this last stage, conclusions are enacted. Use of comparisons is made. On this basis, forecasting is made.

Some Modern Definitions :

From the above two senses of statistics, modem definitions have emerged as given below:

“Statistics is a body of methods for making wise decisions on the face of uncertainty.” —Wallis and Roberts

“Statistics is a body of methods for obtaining and analyzing numerical data in order to make better decisions in an uncertain world.” —Edward N. Dubois

So, from above definitions we find that science of statistics also includes the methods of collecting, organising, presenting, analysing and interpreting numerical facts and decisions are taken on their basis.

The most proper definition of statistics can be given as following after analysing the various definitions of statistics.

“Statistics in the plural sense are numerical statements of facts capable of some meaningful analysis and interpretation, and in singular sense, it relates to the collection, classification, presentation and interpretation of numerical data.”

Related Articles:

• 7 Main Characteristics of Statistics – Explained!
• Use of Statistics in Economics: Origin, Meaning and Other Details
• Nature and Subject Matter of Statistics
• Relation of Statistics with other Sciences

Statistical Papers

Statistical Papers is a forum for presentation and critical assessment of statistical methods encouraging the discussion of methodological foundations and potential applications.

• The Journal stresses statistical methods that have broad applications, giving special attention to those relevant to the economic and social sciences.
• Covers all topics of modern data science, such as frequentist and Bayesian design and inference as well as statistical learning.
• Contains original research papers (regular articles), survey articles, short communications, reports on statistical software, and book reviews.
• High author satisfaction with 90% likely to publish in the journal again.
• Werner G. Müller,
• Carsten Jentsch,
• Shuangzhe Liu,
• Ulrike Schneider

Latest issue

Volume 65, Issue 2

Latest articles

Flexible-dimensional l-statistic for mean estimation of symmetric distributions.

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Some practical and theoretical issues related to the quantile estimators

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Essays on Statistics

Statistics is an irreplaceable learning tool, which you can shed light on in your statistics essay. Statistics essays define it as the collection, processing, accumulation, and analysis of data that characterize education, the country's economy, its culture, and other vital phenomena in the life of society. Term “statistics” derived from the Latin word “status”, which means “a state of affairs”. This term was first used by the German scientist Gottfried Achenwall in 1749. Essays on statistics explore how statistics develops a special methodology for research and processing of materials. Our statistics essay samples will benefit your essay writing – essay samples may help you pick up on some points you might have missed otherwise.

Statistics is the mathematical science involving equations that are used to solve and analyze daily activities in the world around us.  Today, we have great knowledge of the world around us, and this information was collected mathematically through statistics (DeGroot " Schervish, 2012). We can use statistics to tell what...

Skewness Skewness is asymmetrical in a statistical distribution, where the curve appears distorted or concentrated either to the left or to the right. Skewness can be used to define the extent to which a distribution differs from normal distribution. When a curve or distribution in a graph is classical or symmetrical,...

Despite the existence of numerous meanings, outliers are understood as data points which are far outside the standard for a population or a variable. The outlier could be an observation or a reading that is too different from other readings to the extent that it raises suspicion in regards to...

The mean of the data is 14.8 while the standard deviation is 6.7646138. It means that on average, people spend 14.8 hours per week on cleaning. The standard deviation of 6.7646 shows the spread of the data from the actual mean. Using t-statistic, the confidence interval can be given as  S= 6.7646138,...

The type of food eaten determines eating habits of individuals. 2. How DNA affects height. Variables: Independent: DNA                  Dependent: Height Hypothesis: The DNA of an individual has impact on tallness or shortness of a person. Data Analysis How Food affects Habits The appropriate data analysis techniques for the study will be use of Statistical Package for...

The data collected will be analyzed by the researchers who are conducting the study. The researchers will also coordinate the effort of analysis. 2 How will data be analyzed and displayed? The analyzed data will be displayed using tables and graphs. 3 Against what “standards” will you compare your...

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The negative value denotes that the labor cost of $75 was 0.681818 standard deviations lower than the average television repair cost of $90. The z-score for the  $100 labor cost From the z-value, positive  implies that the repair cost was above the mean cost by 0.454545 standard deviations. Question 2 Part a The shaded region...

Primary data simply means the data from the original source with the purpose in mind. It is the kind of data that has not been distorted by a third party unlike the secondary data that can be described as the kind of data that has been collected by any other...

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One area of mathematics called statistics is concerned with gathering, analyzing, and managing data, frequently to make it more understandable and useful. (Brown Kass, 2009). Falsehoods and representational distortions, however, may have an impact on how customers and casual observers interpret data. When presenting data, some sleights of hand...

Score(Award 0 if the incorrect response is provided) Exceeds Normal Expectation 3 (The right response is provided along with strong sources and supporting data. The solution is based on statistical data analysis, reports, previous scientists' research, and other academic papers. highlights the data and statistics that support their response. The...

According to Sammer (2011), adults aged 45 and older made up around 40% of the workforce in the United States. He confirms that the present recession, rising insurance costs, and advancing social security age all contribute to the majority of older Americans working longer than expected (Sammer, 2011). Clearly, the...

Every month, the US Bureau of Labor Statistics calculates the unemployment rate in the United States. The Bureau of Labor Statistics used data from the U.S. Bureau of the Census's Current Population Survey (CPS), which covers 60,000 members of the civilian population over the age of 16. (Marthinsen 73). The unemployment...

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Statistics and probability

Unit 1: analyzing categorical data, unit 2: displaying and comparing quantitative data, unit 3: summarizing quantitative data, unit 4: modeling data distributions, unit 5: exploring bivariate numerical data, unit 6: study design, unit 7: probability, unit 8: counting, permutations, and combinations, unit 9: random variables, unit 10: sampling distributions, unit 11: confidence intervals, unit 12: significance tests (hypothesis testing), unit 13: two-sample inference for the difference between groups, unit 14: inference for categorical data (chi-square tests), unit 15: advanced regression (inference and transforming), unit 16: analysis of variance (anova).

Reflection about Statistics and Probability – Essay Sample [New]

Reflection paper about statistics and probability: introduction, what i learned in statistics and probability, reflection about statistics and probability: data analysis, reflection paper about statistics: future studies, statistics reflection paper: conclusion.

Learning statistics is viewed as an essential subject. It is also crucial to do statistics and probability reflection about their role in math, data management, and one’s daily life as a student. This statistics essay sample is going to cover what I have learned in statistics and probability. Essay will talk about my experience of learning the necessary skills for analyzing data and predicting possible outcomes.

I have extensively studied statistics and probability throughout this course. The probability course appeared to be a useful tool to apply in areas of statistical analysis. However, the part of learning statistics is much more prominent.

Statistical knowledge for both statisticians and non-statisticians is essential (Broers, 2006). So it is recommended that people from all fields be given the necessary statistical skills.

For that kind of reason, to gain quantitative skills to be applied and worked on in many ways, I followed this course. In this regard, I had hoped to acquire knowledge in designing experiments. I had wanted to grow in collecting and analyzing data, interpreting results, and drawing conclusions as well (Broers, 2006). I summarized and analyzed the results in my reflection about statistics and probability.

I can proudly say now that I have learned many useful things. I now understand math applications very clearly. I know how to collect, arrange, and explain the details. In data analysis, I may apply central tendency measurements such as mean, mode, and median.

I may also use dispersion measures to explain the data, such as standard deviation and variance. Furthermore, I have a detailed understanding of probability distribution. I can see what conditions are to be fulfilled for a normal distribution (Broers, 2006).

For example, I am aware of conditional probability and its applications. I also know how to use The Poisson process, Brownian motion process, Stochastic processes, Stationary processes, and Markovian processes. I learned the Ehrenfest model of diffusion, the symmetric random walk, queuing models, insurance risk theory, and Martingale theory.

Now, I can determine the relation between the two data sets. I can distinguish dependent and independent variables as well as the sort of relationship between them. I will tell you whether one random variable is causal to another. I am also able to determine positive, negative, and minimal correlations (Broers, 2006).

In most instances, data collection on an entire population is delicate (Chance, 2002). I got the necessary skills in sampling techniques in this respect. I have the skills to analyze sample data. Now I can draw inferences about the entire population using statistical probabilities and hypothesis testing.

In hypothesis testing, one seeks to determine whether the outcomes of a given sample are due to chance or known cause (Chance, 2002). Knowledge is used in the implementation of significance level, critical value, degrees of freedom, and p-value. One must be able to present the null hypothesis and the alternative hypotheses (Chance, 2002).

Now I’m able to use a t-test to assess if there are statistically significant variations between two data sets. In this regard, I understand the required assumptions for the t-test to be applied. I have a clear insight into the analysis of variance (ANOVA), both single and bidirectional. However, I feel that further practice would improve my knowledge of all of those applications (Chance, 2002).

This program has provided me with a good understanding of how statistics play a major part in life. Among other areas, statistics is the most commonly used research method in medicine, education, psychology, business, and economics (Rumsey, 2002). It helps to shape the choices people make in their everyday lives. Statistical studies may provide a clear picture of the consequences. For example, the results of such activities as smoking and contribute to corrective steps.

I was always keen to build a stable scientific career. I have now decided to major in statistics after taking this course. I would like to have advanced statistical skills that will help me to manage and evaluate complex research problems. The knowledge I’ve already obtained in this case will give me a strong foothold.

The goals I had hoped to accomplish by following this cause were well achieved. Now I can conduct experiments and collect, analyze, and interpret data. In real-life scenarios, I can apply that information and draw conclusions that will help develop answers to some issues.

Also, I have thoroughly studied and understood various causes of probability. I will be able to apply this knowledge where needed. Nevertheless, statistics will remain my main field of research.

This course, therefore, gave me the desire to seek additional statistical knowledge. For this reason, I intend to be in a better position in statistics to deal with more complex research issues.

• Broers, N. J. Learning goals: the primacy of statistical knowledge. 2006, Maastricht: Maastricht University.
• Chance, B. L. Components of statistical thinking and implications for instruction and assessment . 2002, Journal of Statistics Education, 10(3)
• Rumsey, D. J. Statistical literacy as a goal for introductory statistics courses. 2002, Journal of Statistics Education, 10(3)

What should I include in my statistics reflection paper?

Your statistics essay should contain a number of research data. Thoroughly research your subject. You can also include visual support like graphs or diagrams. Make sure the statistics are broken down and provide a general image of the issue.

Why are statistics so difficult?

Much of statistics makes no sense to students as it’s taught out of context. Many people often do not understand anything until they begin to examine data in their studies. You need to gain academic knowledge before you can understand statistics.

How do you start a reflection on statistics?

The good idea is to start your essay on statistics with a choice of the right topic. Make sure to research everything thoroughly and take notes of interesting observations. You should have a detailed understanding of a problem, and work well with data.

What is the aim of statistics?

Statistics aims to help you to use the right methods to gather the data. It ensures you use analysis correctly and present the results effectively. Statistics are essential to make science-based discoveries, make data-based decisions, and predict possible results.

What is the importance of statistics and probability?

Statistics is the mathematics that we use to gather, organize, and interpret numerical information. Probability is the study of possible events. It is often used in the analysis of chance games, genetics, and weather forecasting. A myriad of other everyday occurrences can be examined.

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Why Taiwan Was So Prepared for a Powerful Earthquake

Decades of learning from disasters, tightening building codes and increasing public awareness may have helped its people better weather strong quakes.

Search-and-rescue teams recover a body from a leaning building in Hualien, Taiwan. Thanks to improvements in building codes after past earthquakes, many structures withstood Wednesday’s quake. Credit...

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By Chris Buckley ,  Meaghan Tobin and Siyi Zhao

Photographs by Lam Yik Fei

Chris Buckley reported from the city of Hualien, Meaghan Tobin from Taipei, in Taiwan.

• April 4, 2024

When the largest earthquake in Taiwan in half a century struck off its east coast, the buildings in the closest city, Hualien, swayed and rocked. As more than 300 aftershocks rocked the island over the next 24 hours to Thursday morning, the buildings shook again and again.

But for the most part, they stood.

Even the two buildings that suffered the most damage remained largely intact, allowing residents to climb to safety out the windows of upper stories. One of them, the rounded, red brick Uranus Building, which leaned precariously after its first floors collapsed, was mostly drawing curious onlookers.

The building is a reminder of how much Taiwan has prepared for disasters like the magnitude-7.4 earthquake that jolted the island on Wednesday. Perhaps because of improvements in building codes, greater public awareness and highly trained search-and-rescue operations — and, likely, a dose of good luck — the casualty figures were relatively low. By Thursday, 10 people had died and more than 1,000 others were injured. Several dozen were missing.

“Similar level earthquakes in other societies have killed far more people,” said Daniel Aldrich , a director of the Global Resilience Institute at Northeastern University. Of Taiwan, he added: “And most of these deaths, it seems, have come from rock slides and boulders, rather than building collapses.”

Across the island, rail traffic had resumed by Thursday, including trains to Hualien. Workers who had been stuck in a rock quarry were lifted out by helicopter. Roads were slowly being repaired. Hundreds of people were stranded at a hotel near a national park because of a blocked road, but they were visited by rescuers and medics.

On Thursday in Hualien city, the area around the Uranus Building was sealed off, while construction workers tried to prevent the leaning structure from toppling completely. First they placed three-legged concrete blocks that resembled giant Lego pieces in front of the building, and then they piled dirt and rocks on top of those blocks with excavators.

“We came to see for ourselves how serious it was, why it has tilted,” said Chang Mei-chu, 66, a retiree who rode a scooter with her husband Lai Yung-chi, 72, to the building on Thursday. Mr. Lai said he was a retired builder who used to install power and water pipes in buildings, and so he knew about building standards. The couple’s apartment, near Hualien’s train station, had not been badly damaged, he said.

“I wasn’t worried about our building, because I know they paid attention to earthquake resistance when building it. I watched them pour the cement to make sure,” Mr. Lai said. “There have been improvements. After each earthquake, they raise the standards some more.”

It was possible to walk for city blocks without seeing clear signs of the powerful earthquake. Many buildings remained intact, some of them old and weather-worn; others modern, multistory concrete-and-glass structures. Shops were open, selling coffee, ice cream and betel nuts. Next to the Uranus Building, a popular night market with food stalls offering fried seafood, dumplings and sweets was up and running by Thursday evening.

Earthquakes are unavoidable in Taiwan, which sits on multiple active faults. Decades of work learning from other disasters, implementing strict building codes and increasing public awareness have gone into helping its people weather frequent strong quakes.

Not far from the Uranus Building, for example, officials had inspected a building with cracked pillars and concluded that it was dangerous to stay in. Residents were given 15 minutes to dash inside and retrieve as many belongings as they could. Some ran out with computers, while others threw bags of clothes out of windows onto the street, which was also still littered with broken glass and cement fragments from the quake.

One of its residents, Chen Ching-ming, a preacher at a church next door, said he thought the building might be torn down. He was able to salvage a TV and some bedding, which now sat on the sidewalk, and was preparing to go back in for more. “I’ll lose a lot of valuable things — a fridge, a microwave, a washing machine,” he said. “All gone.”

Requirements for earthquake resistance have been built into Taiwan’s building codes since 1974. In the decades since, the writers of Taiwan’s building code also applied lessons learned from other major earthquakes around the world, including in Mexico and Los Angeles, to strengthen Taiwan’s code.

After more than 2,400 people were killed and at least 10,000 others injured during the Chi-Chi quake of 1999, thousands of buildings built before the quake were reviewed and reinforced. After another strong quake in 2018 in Hualien, the government ordered a new round of building inspections. Since then, multiple updates to the building code have been released.

“We have retrofitted more than 10,000 school buildings in the last 20 years,” said Chung-Che Chou, the director general of the National Center for Research on Earthquake Engineering in Taipei.

The government had also helped reinforce private apartment buildings over the past six years by adding new steel braces and increasing column and beam sizes, Dr. Chou said. Not far from the buildings that partially collapsed in Hualien, some of the older buildings that had been retrofitted in this way survived Wednesday’s quake, he said.

The result of all this is that even Taiwan’s tallest skyscrapers can withstand regular seismic jolts. The capital city’s most iconic building, Taipei 101, once the tallest building in the world, was engineered to stand through typhoon winds and frequent quakes. Still, some experts say that more needs to be done to either strengthen or demolish structures that don’t meet standards, and such calls have grown louder in the wake of the latest earthquake.

Taiwan has another major reason to protect its infrastructure: It is home to the majority of production for the Taiwan Semiconductor Manufacturing Company, the world’s largest maker of advanced computer chips. The supply chain for electronics from smartphones to cars to fighter jets rests on the output of TSMC’s factories, which make these chips in facilities that cost billions of dollars to build.

The 1999 quake also prompted TSMC to take extra steps to insulate its factories from earthquake damage. The company made major structural adjustments and adopted new technologies like early warning systems. When another large quake struck the southern city of Kaohsiung in February 2016, TSMC’s two nearby factories survived without structural damage.

Taiwan has made strides in its response to disasters, experts say. In the first 24 hours after the quake, rescuers freed hundreds of people who were trapped in cars in between rockfalls on the highway and stranded on mountain ledges in rock quarries.

“After years of hard work on capacity building, the overall performance of the island has improved significantly,” said Bruce Wong, an emergency management consultant in Hong Kong. Taiwan’s rescue teams have come to specialize in complex efforts, he said, and it has also been able to tap the skills of trained volunteers.

Taiwan’s resilience also stems from a strong civil society that is involved in public preparedness for disasters.

Ou Chi-hu, a member of a group of Taiwanese military veterans, was helping distribute water and other supplies at a school that was serving as a shelter for displaced residents in Hualien. He said that people had learned from the 1999 earthquake how to be more prepared.

“They know to shelter in a corner of the room or somewhere else safer,” he said. Many residents also keep a bag of essentials next to their beds, and own fire extinguishers, he added.

Around him, a dozen or so other charities and groups were offering residents food, money, counseling and childcare. The Tzu Chi Foundation, a large Taiwanese Buddhist charity, provided tents for families to use inside the school hall so they could have more privacy. Huang Yu-chi, a disaster relief manager with the foundation, said nonprofits had learned from earlier disasters.

“Now we’re more systematic and have a better idea of disaster prevention,” Mr. Huang said.

Mike Ives contributed reporting from Seoul.

Chris Buckley , the chief China correspondent for The Times, reports on China and Taiwan from Taipei, focused on politics, social change and security and military issues. More about Chris Buckley

Meaghan Tobin is a technology correspondent for The Times based in Taipei, covering business and tech stories in Asia with a focus on China. More about Meaghan Tobin

Siyi Zhao is a reporter and researcher who covers news in mainland China for The Times in Seoul. More about Siyi Zhao

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Caitlin Clark Had Classy Gesture for Fans While Leaving Court After Iowa’s Loss to South Carolina

• Author: Karl Rasmussen

In this story:

Iowa superstar Caitlin Clark played her final college basketball game on Sunday, ending her career in with a crushing defeat against Dawn Staley's undefeated South Carolina team in the National Championship , 87–75.

In the aftermath of the final defeat of her historic career, Clark displayed nothing but class, and she bid farewell to her faithful fans one last time before exiting the court.

Amid the agony of defeat—the second time in as many years that Iowa has come up shy in a national championship scenario—Clark could be seen gesturing to her fans, pointing to her heart in order to show them love before heading to the tunnel.

Caitlin Clark’s final NCAA walk pic.twitter.com/gfucvo8QAd — Gifdsports (@gifdsports) April 7, 2024

Clark scored a game-high 30 points, including five threes, while adding eight rebounds and five assists. She played every minute of the game, but her performance wasn't enough to topple the Gamecocks, who won all 38 games they played this season.

The 22-year-old set records throughout the Hawkeyes' tournament run, and although it wasn't the curtain call she'd hoped for, Clark made sure to show her appreciation for her supporters and was all class on her way off the court.

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NYPD ANNOUNCES CITYWIDE CRIME STATISTICS FOR MARCH, FIRST QUARTER 2024

April 3, 2024

Substantial reductions attained in subway system while shootings, major crime categories continue downward trends

New York City saw continued reductions in overall crime through the first quarter of 2024, both above ground, on streets throughout the five boroughs, and below ground, within the nation’s largest subway system. The single month of March 2024, compared to the same month last year, experienced even more drastic crime declines.

Overall crime in the transit system plummeted 23.5 percent in March, an achievement directly attributable to the 1,000 additional uniformed NYPD officers surged into the network each day. Another 800 NYPD officers were also recently deployed as part of “Operation Fare Play,” an initiative focused on enforcing fare evasion. The year-over-year crime decrease was led by double-digit percentage drops in major categories: Robbery was reduced 51.9 percent (26 vs. 54), grand larceny decreased 15.2 percent (89 vs. 105), and felony assault dropped 10.9 percent (49 vs. 55). From January 1 through March 31, 2024, overall crime in the transit system was down 1.1 percent (538 vs. 544), compared to the first quarter of 2023.

Since the start of 2024, overall arrests in the subway system are up almost 53 percent compared to last year (4,813 vs. 3,147), including an 83.3 percent increase in gun arrests (22 vs. 12), a nearly 80 percent jump in fare-evasion arrests (1,864 vs. 1,038), and a 24.1 percent hike in grand larceny arrests (108 vs. 87). In that time frame, Criminal Court summonses issued by police jumped 65.3 percent (1,666 vs. 1,008), and included an increase of nearly 5.5% (370 vs. 351) in those written specifically for fare evasion. The total number of Transit Adjudication Bureau (TAB) summonses issued for various offenses also climbed 28.1% (48,771 vs. 38,082).

“There cannot be a sense of lawlessness in the subway system, and it begins at the turnstiles,” said Police Commissioner Edward A. Caban . “It is highly encouraging to see the tangible results of our hard work – the investment we are making is clearly paying dividends. We vow to maintain our tight focus on the drivers of crime in order to improve transportation safety – and perceptions of safety – at every station, on every train, at all hours of the day and night. That is what New Yorkers expect and deserve.”

Citywide in March 2024 compared to March 2023, overall crime dropped 5 percent, a reduction of 505 incidents. Continued declines were recorded across many bellwether crimes, including murder, down 19.4 percent (29 vs. 36); burglary, down 17.4 percent (1,005 vs. 1,217); and grand larceny, down 7 percent (3,883 vs. 4,176). Robbery was flat in March (1,264 vs. 1,264), while grand larceny auto – the theft of motor vehicles – declined for the fourth month in a row, down 10.9 percent (1,037 vs. 1,164). From January 1 through the end of the first quarter of 2024, major crime and violence throughout the five boroughs dropped 2.4 percent, a decrease of 711 incidents.

Shooting incidents in March 2024 were reduced 25.9 percent (63 vs. 85), equating to 29 fewer shooting victims compared to the same month last year (71 vs. 100), a 29 percent decrease. This correlates to 358 people arrested for possession of an illegal firearm, a 7.5 percent increase from the same period last year. Shooting incidents for the first quarter of 2024 compared to 2023 were down 18.5 percent (181 vs. 222), meaning that 56 fewer people (212 vs. 268) were shot in New York City since the start of the year, a 20.9 percent reduction. From January 1 through the end of March, the NYPD took nearly 1,600 illegal guns off New York City streets, adding to the 15,180 total guns seized since the start of 2022.

In March 2024, compared to the previous March, the total number of bias incidents investigated by the NYPD’s Hate Crime Task Force across the five boroughs increased by 27 incidents. Overall crime in New York City public housing developments dropped 6.2 percent.

For all major index crimes in March, 479 additional people were arrested compared to a year ago, an 11 percent increase (4,826 vs. 4,347). Since the start of the year, 1,398 more people were arrested for major crimes this year, marking an 11.1 percent jump (13,980 vs. 12,582).

*All crime statistics are preliminary and subject to further analysis, revision, or change.*

Index Crime Statistics: March 2024

Index Crime Statistics: Q1 (Jan. 1 – March 31)

Additional Statistics: March 2024

Additional statistics: q1 (jan. 1 – march 31)    , rape incident reporting statistics: march   2024.

(Reports filed from March 1 – March 31 in years indicated)

Rape continues to be underreported. If you are a victim of sexual assault, please come forward. The 24-hour NYPD Special Victims Division hotline is: 212-267-RAPE (7273).

Hate Crimes Statistics: March 2024

(Representing March 1 – March 31 for calendar years 2024 and 2023)

Note: Statistics above are subject to change upon investigation, as active possible bias cases may be reclassified to non-bias cases and removed from counted data.

Filing Season Statistics Show Refunds Edging Higher As Tax Day Approaches

As of March 22, 2024, the IRS had received 80,470,000 tax returns, compared to 80,683,000 returns received as of March 24, 2023, a .3% decline. That suggests that taxpayers aren’t in a hurry to file.

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Alarm clock

Tax filing season statistics still suggest that filers aren’t rushing to file their returns—but tax refunds are continuing their upward trend.

Tax Filing Season Data

The IRS had previously announced that they expected more than 128.7 million individual tax returns to be filed by Tax Day, April 15, 2024.

Some of that could be attributable to the weather—the spring hasn’t been kind to many parts of the country—but it’s more likely that taxpayers who might have been impacted by pending legislation put filing on hold. Not only would the Tax Relief for American Families and Workers Act expand the child tax credit retroactively to the 2023 tax year, it would help small and private businesses by allowing immediately expensing of domestic research and experimental expenditures, providing for 100% bonus depreciation for qualifying property, and loosening the interest expense limitation rules.

The bill was announced in mid-January and passed the House at the end of the month with considerable bipartisan support (357-70). The bill has stalled in the Senate and no vote has been scheduled.

Despite the uncertainty that the bill will advance, IRS Commissioner Danny Werner has encouraged taxpayers to file anyway , saying that the IRS will make any necessary changes. Nonetheless, some taxpayers may have opted to extend.

Filing Season Statistics, week ending March 22, 2024

The rate of processing is also a bit behind last year’s numbers. IRS tax season data shows that the IRS has processed 79,243,000 individual income tax returns as of March 22, 2024, as compared to 80,369,000 by March 24, 2023. That's a decrease of 1.4%.

Just under half—about 48%—of e-filed returns have been self-prepared. That percentage has dropped as the season progresses, which isn’t unusual. Professionally prepared returns—those accounted for 40,311,000 of e-filed returns received so far in 2024—tend to pick up as the season rolls on.

A significant majority of the returns received to date—just under 97%—were e-filed. That number is slightly lower than earlier in the tax season and will likely settle. The IRS encourages taxpayers to file electronically, noting that taxpayers who e-file and use direct deposit typically see a refund within 21 days.

Web usage, IRS.gov visits, week ending March 22, 2024

Web visits to IRS.gov continued to climb, increasing by 19.0% compared to last year. There have been 441,085,000 visits to the website as of March 22, 2024, compared to 370,706,000 visits as of March 24, 2023.

Taxpayers could be clicking over to check out new services. The IRS has been ramping up its online capabilities for individual taxpayers, business taxpayers , and tax professionals . The IRS encourages taxpayers to log in and resolve taxpayer account issues online, when possible. With online access, individual taxpayers can access tax records, make and view payments (including scheduling and canceling payments), view or create payment plans (including expanding and revising plans), view their balance, and manage communication preferences. You can also save multiple bank accounts, validate bank account information, and display bank names.

Taxpayers may also be using the website more often to check the status of their tax refunds. The IRS reminds taxpayers that Where's My Refund? remains the best way to check the status of a refund. Refund status information is typically available within 24 hours after the IRS receives your e-filed tax return for the current tax year, three to four days after receipt of your e-filed tax return for the tax years 2022 or 2021, or four weeks after mailing your paper return.

The IRS only updates the tool once a day, usually overnight.

The number of refunds issued remains lower those from last year. The IRS has issued 54,990,000 tax refunds as of March 22, 2024, compared to 59,342,000 tax refunds issued as of March 24, 2023, a decrease of 7.3%. That works out to $169.411 billion in total refunds, compared to $172.263 billion in 2023, a decrease of 1.7%.

Tax Refund Statistics, week ending March 22, 2024

The average tax refund has edged up—it’s $3,081 compared to last week’s $2,903 per taxpayer from last year.

Most of those refunds were issued via direct deposit. The total number of direct deposit refunds issued was 52,795,000, as of March 22, 2024, a decline of 5.6%. Overall, the total amount refunded with direct deposit sit at $166.424 billion, a .5% decline. But, the average direct deposit refund was a little higher than the prior year, weighing in $3,152, compared to the previous year amount of $ 2,991, a 5.4% increase.

Tax Day is April 15, 2024—it will be here before you know it. Check back as the season progresses for updated numbers.

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