Introducing Statistics: What Can We Learn from Data?

What a statistical study is

A statistical study collects data from a sample to answer a question about a larger population. The population is every item or individual you want to know about. The sample is the part of the population that data are actually collected from.

Studies use samples because measuring a whole population is usually out of reach. Sometimes the population is simply too large: every teenager in the country, every phone a company sold last year. Sometimes collecting data from every member is too difficult. Some measurements destroy what they measure, like counting the chips in a cookie or crash-testing a car, and some people are hard to find or never answer.

A few words and symbols come up constantly:

• A datum is one piece of information about one item or individual, such as one cookie's chip count. A collection of data is a data set.
• $N$ is the population size, here the 50,000 cookies.
• $n$ is the sample size, the number of cookies the bakery actually breaks apart.

Say it in context

Every number in a study is about something real. A mean of 214 means nothing until you say what was measured, on whom, and in what units. Answering in context means tying each part of a study, and each calculation, back to the real situation it came from.

Compare two sentences about the same number:

• "The mean is 214."
• "The 400 sampled teens spent a mean of 214 minutes outdoors last weekend."

The first could be about anything. The second names the variable, the units and the group, so a reader can tell whether it matters to them.

Investigative questions

Every study starts with an investigative question, the question the data are collected to answer. It is a question about a population, where values differ from one individual to the next. "How long did Jada sleep last night?" needs no study; you would just ask Jada. "How long do students at our school sleep on a school night?" does.

Fix the purpose before you see the data. The question for a study is set when the study is planned, and it does not change because of the analysis or the results. Rewrite the question to fit whatever turned up and you can make almost any data set look like it found something. A pattern you notice along the way is a good reason to plan a new study, with new data.

Ask for data you can actually collect and analyze. "Do students at our school spend too much time on their phones?" sounds fine until you try to measure too much. "What is the mean daily screen time, in hours, for students at our school?" names a quantity you can record for each student and summarize.

A complete investigative question has three components, and 1.10 The Investigative Question Revisited and Data Collection builds them out. These two rules are enough to spot a question that will not work.