Statistical Questions with Categorical Answers
A statistical question is one designed to collect data that will vary across a group, including questions with non-numerical (categorical) answers like 'yes' or 'no' or color preferences. 'Do you have a pet?' is a statistical question because different people give different answers. 'What is 5 + 3?' is not a statistical question because it has one fixed answer. This Grade 7 math skill from Saxon Math, Course 2 introduces statistical thinking, helping students distinguish between fixed mathematical questions and data-collection questions that show variability across a population.
Key Concepts
Property A statistical question can have non numerical answers, such as ''Yes'' or ''No''. The question is statistical as long as you expect to get a variety of answers when you ask a group of people.
Examples Is "Do you own a pet?" a statistical question? Yes, because asking a group of people will result in a variety of ''Yes'' and ''No'' answers. Is "What is your favorite color?" a statistical question? Yes, because you anticipate different people will have different favorite colors (e.g., blue, red, green). Is "Is the school mascot a tiger?" a statistical question? No, this is a question with a single correct answer (either it is or it isn''t), so there is no variability in the data.
Explanation A statistical question is one that anticipates variability in the data collected. This variability can exist even when the answers are categories rather than numbers. For example, a ''Yes/No'' question asked to a group of people is statistical because you don''t expect everyone to give the same answer. The key is that the answer can change from one individual to the next.
Common Questions
What is a statistical question?
A statistical question is one that anticipates variability in the answers when asked of multiple people or measured across multiple cases. 'How many hours do students sleep?' is statistical because answers vary.
Can statistical questions have non-numerical answers?
Yes. 'What is your favorite color?' and 'Do you exercise daily?' are statistical questions with categorical (non-numerical) answers, because different people give different responses.
How do I tell if a question is statistical or not?
A question is statistical if you expect a variety of answers from different people or situations. If there is only one possible correct answer (like a math fact), it is not statistical.
What is an example of a non-statistical question?
'How many inches are in a foot?' has one fixed answer (12). It is not statistical because there is no variability — the answer is always the same.
When do students learn about statistical questions?
Statistical questions are introduced in Grade 6-7 as the foundation of data analysis. Saxon Math, Course 2 covers them in Chapter 10.
Why does it matter whether a question is statistical?
Only statistical questions generate data worth analyzing with measures of center, spread, and graphical displays. Identifying statistical questions is the first step in planning a data investigation.
How do statistical questions with categorical answers differ from those with numerical answers?
Categorical answers (yes/no, colors, types) are displayed with bar graphs or pie charts. Numerical answers (heights, scores, ages) are displayed with histograms, dot plots, or box plots.