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We often collect data to answer questions about something. The data we collect may show variability, which means the data values are not all the same.
Some data sets have more variability than others. Here are two sets of figures.
Set A has more figures with the same shape, color, or size. Set B shows more figures with different shapes, colors, or sizes, so Set B has greater variability than Set A.
Both numerical and categorical data can show variability. Numerical sets can contain different numbers, and categorical sets can contain different categories or types.
When a question can be answered only by using data, and we expect that data to have variability, we call it a statistical question. Here are some examples.
To answer the question about books, we may need to count all of the books in each classroom of a school. The data we collect would likely show variability because we would expect each classroom to have a different number of books.
In contrast, the question “How many books are in your classroom?” is not a statistical question. It would only require one person to count the books to get the answer, so there is no variability. Likewise, if we ask all of the students at a school where they go to school, that question is not a statistical question because the responses will all be the same.
A statistical question can be answered by collecting data that has different values. Here are some examples of statistical questions:
The variability of a data set describes how different the values are.
Data set B has many different values, while data set A has more of the same values. So, data set B has more variability.