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# Identifying Statistical Questions

## Task

Which of the following are statistical questions? (A statistical question is one that can be answered by collecting data and where there will be variability in that data.)

- How many days are in March?
- How old is your dog?
- On average, how old are the dogs that live on this street?
- What proportion of the students at your school like watermelons?
- Do you like watermelons?
- How many bricks are in this wall?
- What was the temperature at noon today at City Hall?

## IM Commentary

Statistics is the study of variability. Students need to be able to identify and pose questions that can be answered by data that vary. The purpose of this task is to help students learn to distinguish between statistical questions and questions that are not statistical. A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question. We would answer this question by collecting data from 6th graders, and we expect that not all 6th grade students spend the same amount of time on homework (meaning there will be variability in the data). On the other hand, "How much time did Juana spend on homework last night?" is not a statiscal question--it has a deterministic answer and is not answered by collecting data that vary.

## Solution

- Not statistical. This question is answered by counting the number of days in March. This produces a single number. This question is not answered by collecting data that vary.
- Not statistical. This question is answered by a single number. It is not answered by collecting data that vary.
- Statistical. This question would be answered by collecting data, and there would be variability in that data.
- Statistical. This question would be answered by collecting data, and there would be variability in that data.
- Not statistical. This question is answered by a single response. It is not answered by collecting data that vary.
- Not statistical. This question would be answered by counting the bricks. This produces a single number. This question is not answered by collecting data that vary.
- Non-statistical (there is one temperature).

## Identifying Statistical Questions

Which of the following are statistical questions? (A statistical question is one that can be answered by collecting data and where there will be variability in that data.)

- How many days are in March?
- How old is your dog?
- On average, how old are the dogs that live on this street?
- What proportion of the students at your school like watermelons?
- Do you like watermelons?
- How many bricks are in this wall?
- What was the temperature at noon today at City Hall?

## Comments

Log in to comment## KATT says:

over 1 yeardeez nuts

## roxypeck says:

over 1 yearTask edited 2/29/16 to clarify question posed in part g. This question is not a statistical question because there is no variability in the data that would be used to answer this question.

## cameron says:

over 2 yearsremoved

## roxypeck says:

over 2 yearsThanks for your comment. I have edited the task to try to frame the questions in a way that makes it more straightforward to determine if a given question is a statistical question or not.

What makes (e) not a statistical question is that it is asking about one particular person. It would be answered by asking that person, resulting in a single observation rather than a set of data that vary. In contrast, (d) is a statistical questions as it would be answered by surveying many people, resulting in a set of data that would vary (the response would vary from person to person). The question posed in (e) might be the "survey question" that you would use to collect the data to answer the question in (d), but by itself and referring to just one specific person, it would not be considered a statistical question. Hope that helps.

## Shelbi says:

about 3 yearsWe'd like some more perspectives on the questions presented on this list. Is (d) a statistical question or is (e) a statistical question? Isn't (e) the statistical question you would use to help answer (d)? There are lots of statistical analyses intended for questions that have dichotomous answer choices. If dichotomous questions where some people are likely to answer yes and others no are not statistical, then what constitutes variability? Three possible answers? Infinite? I wonder if we can improve the framing of tasks by situating the questions a bit better. Or maybe having "possible data sets" that map back to the question (eg, match each response set with the question that likely generated it).