Practice Comparative Statistics in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Comparative statistics involves using statistical measures to compare two or more groups, data sets, or distributions.

Is A bigger/better/different than B? By how much? Is the difference real?

Example 1

easy
Compare two groups on a test: Group A (n=30): mean=75, SD=10. Group B (n=30): mean=82, SD=8. Calculate the difference in means and comment on whether group B performs better.

Example 2

medium
Three products have customer satisfaction scores. Product A: mean=4.2, SD=0.5 (n=50). Product B: mean=3.8, SD=1.2 (n=50). Explain which product is preferable and why SD matters.

Example 3

easy
Box plots for two classes show: Class A median=70, IQR=20. Class B median=75, IQR=5. Which class has better performance? Which is more consistent?

Example 4

hard
Men: mean height = 70", SD = 3". Women: mean height = 64", SD = 2.5". A person is 67" tall. Calculate their z-score in each distribution and determine which group they are more extreme in.
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