Explainer: Statistical and Nonstatistical Questions

In this explainer, we will learn how to differentiate between statistical and nonstatistical questions.

We will start with the definition and then look at examples to help us understand the definition.

Definition: Statistical Questions

A statistical question is a question that can be answered by gathering data and a question for which we expect to have variation in the data we collect.

Example 1: Deciding Whether a Question Is Statistical

Determine whether the following is a statistical question: How tall are you?

Answer

To answer this question, we just have to record one height. There will be no variability in the data which means that it is not a statistical question.

Example 2: Deciding Whether a Question Is Statistical

Determine whether the following is a statistical question: What are the heights of the players of your favorite soccer team?

Answer

The answer to this question would be a list of the heights of the players on the team. We expect that there will be variability in the data we collect because not everyone will be the same height. Therefore, this is a statistical question.

Example 3: Deciding Whether a Question Is Statistical

Determine whether the following is a statistical question: In general, how tall are humans?

Answer

An answer to this question could be the mean of the heights of a sample of humans. Therefore, to answer it, we need to collect the data which tells us the heights of different people. Since people are of different heights, there will be variability in the data we collect. Hence, it is a statistical question.

In the above examples, we saw that a statistical question can be answered by a list of data like the heights of a group of people or by a single value that summarizes a set of varied data, like the mean of people’s heights. A question is not statistical if the data we collect to answer it is a single value.

Note that the data collected to answer statistical questions does not have to be numerical. There are two types of data we could collect: numerical and categorical.

Definition: Numerical and Categorical Data

  • In a numerical data set, all of the data values are numbers. For example, data sets summarizing ages, weights, or heights contain numerical data.
  • In a categorical data set, the data can be grouped into categories. For example, a data set recording the eye colors of a group of people contains categorical data and each eye color can be thought of as a category.

The first three examples we considered contained questions that could be answered by numerical data. These last two example shows questions that would be answered by categorical data.

Example 4: Deciding Whether a Question Is Statistical

Determine whether the following is a statistical question: What is your favorite subject?

Answer

The answer to this question is a single subject; we do not have to collect data with variability to answer the question. Therefore, it is not a statistical question.

Example 5: Deciding Whether a Question Is Statistical

Determine whether the following is a statistical question: How do students travel to school?

Answer

To answer this question, we would have to collect data about how students travel to school: by car, bike, or bus for example. Since we expect the students’ answers to vary, this is an example of a statistical question.

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