Statistics is a branch of mathematics that allows us to analyze and interpret numerical data.

Purely mathematical statistics, or statistical inference, is often distinguished from descriptive statistics, which deals with the collection, analysis, presentation, and summarization of data. In this course we will teach you the basic notions of descriptive statistics. Descriptive statistics helps you summarize large amount of numerical data.

Imagine that you work for a party equipment store and you're in charge of sales of balloons. Here are the January sales of balloons (we only show the first 10 out of nearly 10000 purchases for this month):

How do you make sense of this list of numbers? Are the sales generally small or large? Are there any patterns in the sales? Are some quantities more popular than other? You can answer these questions with a knowledge of descriptive statistics.

Remember: descriptive statistics helps us summarize large amounts of data.

Here are some other situations when the knowing descriptive statistics can help you:

• You're a teacher and your students have just completed a quiz. How do you summarize quiz results? Did the students did well on the quiz as a group? What is the best score? What is the worst score?
• You keep track of your grocery expenses. How much do you spend on groceries on a typical day? What is the maximum amount of your grocery spending? What is the minimum amount?

Descriptive statistics can help you compare two data sets. Returning to our balloon example, suppose another month has passed, so now you have data for both January and February sales. Are the sales in the two months generally the same? Have the sales generally increased or decreased? Again, these are questions descriptive statistics can help address.

Remember: descriptive statistics helps us compare two different datasets.

Other examples along the same lines:

• You're a teacher and you want to compare your students with the group from the previous year. Did the current group do better or worse?
• You want to compare this month's expenses to those of the last month. Did you spend more or less? Do the monthly expenses share a pattern, or are they completely different?

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