Case Study

Explain to the student researcher why a categorical variable like 'sex' can have a distribution, and explain how the counts of 4444 and 5656 demonstrate this distribution within their sample.

Case context: A student researcher is analyzing demographic data for a sample of 100100 university students. They record that 4444 students score as 'male' and 5656 score as 'female'. The researcher is confused because they believe that only quantitative (numerical) variables can have a distribution, and they are unsure how to interpret these categorical counts in terms of a distribution.

Question: Explain to the student researcher why a categorical variable like 'sex' can have a distribution, and explain how the counts of 4444 and 5656 demonstrate this distribution within their sample.

Sample answer: Categorical variables like 'sex' can have distributions. The distribution of any variable, including categorical ones, is simply the frequency of each score or category within the sample. In this case, the counts of 4444 'male' and 5656 'female' represent the specific distribution of 'sex' across the 100100 students, showing how the sample is split between the two categories.

Key points:

  • Categorical variables (such as 'sex') can have distributions.
  • A distribution displays the frequencies or counts of individuals across the different categories of a variable.
  • The counts of 4444 'male' and 5656 'female' students represent the specific distribution of the variable 'sex' in the sample of 100100.

Rubric: The response must explain: 1. That categorical variables can have distributions (1 point). 2. That a distribution shows the frequency of scores/categories in a sample (1 point). 3. That the specific counts (4444 'male' and 5656 'female') display the distribution of the variable 'sex' within the 100100 student sample (1 point).

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Updated 2026-05-26

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Research Methods in Psychology - 4th American Edition @ KPU

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