1.1: What is Statistics?
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- Define statistics
Introduction to Statistics
Statistics includes numerical facts and figures. For instance:
- The largest earthquake measured \(9.5\) on the Richter scale.
- In \(2023\), \(83\%\) of all adult homicide victims were male.
- in \(2023\), about a quarter of women of reproductive age in South Africa were HIV positive.
- By the year \(2050\), there will be \(82\) million people aged \(65\) and over in the United States, a \(47\)% increase since \(2022\).
The study of statistics uses math and different types of calculations, but it is based on much more than that. Statistics also includes ideas and methods that help us, as researchers, ask good questions, collect data, analyze it, and understand what it means. Below are three examples where people make claims based on numbers. In each case, the numbers might be accurate, but the conclusion is incorrect. Try to identify the main problem in each example before checking the explanation.
A new Ben and Jerry's ice cream advertisement came out in late May last year. Over the next three months, ice cream sales went up by \(30\%\), so the company claimed that the advertisement was effective.
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A major problem with this conclusion is that ice cream sales naturally go up in June, July, and August, no matter what ads are shown. This is called a history effect, and it happens when people think one thing caused a result, even though another factor (like the time of year) is actually responsible.
The more churches there are in a city, the more crime there is. Therefore, churches lead to crime.
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A major problem with this conclusion is that both the number of churches and the amount of crime increase when a city has a larger population. This is an example of a third-variable problem, where people mistakenly think two things cause each other when a separate factor is actually causing both. In this case, the population size is impacting the number of churches and the crime rate.
At Harvard, the percentage of seniors that graduated with a GPA of \(4.0\) increased nearly \(78\%\) from \(2020\) to \(2023\). Thus, grade inflation is a real epidemic.
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A major problem here is that we don't have the information that we need. What are the actual graduation rates they are comparing? For example, if only \(1\%\) of students earned a \(4.0\) GPA in \(2020\) and \(1.78\%\) earned a \(4.0\) in \(2023\), then \(1.78\%\) is \(78\%\) higher than \(1\%.\) But that increase is still very small and does not prove that grade inflation is a big problem. Also, this statistic doesn't tell us whether the number of \(4.0\) GPAs changed a lot from year to year for other reasons. Overall, there is simply not enough information to fully understand the impact of the statistic. If you're interested, read more about the statistics of graduating seniors here.
Overall, these examples show that "statistics" are not only facts and figures. In the broadest sense, statistics includes many methods for analyzing, interpreting, displaying, and making decisions based on data.