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Statistics is a tricky business. The casual reader doesn't understand statistics in any great depth, while the experienced reader often knows a lot about the subject. Balancing between these two extremes is often difficult, and far from natural. The following resource is meant as a guide to writing statistics.

This guide is not meant to teach you statistics, but rather how to use statistics more effectively in your writing. This guide is designed to help you understand both how to write using other people's statistics, and how to write using your own statistics. If you want to learn how to interpret statistics, then take a course taught by a professional. For an excellent beginner's textbook, see Introduction to the Practice of Statistics by David S. Moore and George P. McCabe.

### What is a Statistic?

In the casual sense, a statistic is any number that describes a group of objects. There are two main categories of statistics, descriptive and inferential.

• Descriptive: Statistics that merely describe the group they belong to.
• Inferential: Statistics that are used to draw conclusions about a larger group of people.

Examples of Descriptive Statistics

The class did well on its first exam, with a mean (average) score of 89.5% and a standard deviation of 7.8%.
This season, the Big High School Hockey Team scored a mean (average) of 2.3 goals per game.

Many times, however this group of objects is a smaller subset of a larger group. By examining the smaller subset, it is often thought that information can be inferred upon the larger population. This is the basis of inferential statistics.

Examples of Inferential Statistics

According to our recent poll, 43% of Americans brush their teeth incorrectly.
Our research indicates that only 33% of people like purple cars.

In these last two examples, the researchers have not studied all people, they have studied a small group of people, and are generalizing the results to lots of people. This is known as inferential statistics, because you are inferring properties about a large group from a smaller group. As a statistician or a researcher, it is your hope that this smaller group is representative of the larger group, and that the two groups behave the same way. If they do not, then your inference may not be correct.

If you merely want to describe the data that you have for one single group, then you are using descriptive statistics. If you want to say something about a larger group, or you want your reader to infer something about a larger group, then you need to use inferential statistics. It is important to understand the difference between these two because how you use a statistic depends on what type of statistic it is.