Statistics Practice Problems

1. Describing one data set. Find mean, median, and mode from a list of values, then separate range from interquartile range using the quartiles.
2. Comparing two data sets. Use standard deviation to judge which group is more consistent when both share the same mean.
3. Probability. Work with a complementary event, then read a conditional probability off a two-way table where the condition changes the denominator.
4. Study design and reasoning. Spot who a convenience sample leaves out, and explain why a positive association in a scatterplot still does not establish cause.
5. Normal distribution and inference. Convert a raw score to a z-score, apply the 68–95–99.7 rule, and interpret a confidence interval built from a sample proportion.

1. Separate computation errors from interpretation errors. Missing the IQR question is a procedure gap. Missing the sampling or causation question is a reasoning gap, and it needs discussion rather than more drill.
2. Write out the quartiles before finding IQR. Most range and IQR mistakes come from splitting the data set incorrectly, not from the subtraction at the end.
3. Say conditional probabilities out loud. “Given that the student plays a sport” means the total shrinks to only those students. Naming the new denominator before calculating prevents the most common error on these questions.
4. Practice the procedures that repeat. Our math worksheets give repeated work on averages, spread, and probability calculations.
5. Get help with the reasoning questions. A statistics tutor can work through study design, inference, and what a confidence interval actually claims — the parts that are hardest to learn from an answer key.

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Tests Interpretation, Not Only Calculation

Four of the ten problems ask what the numbers mean rather than what they equal — which class is more consistent, who a survey misses, whether a pattern proves cause. Students who can compute but cannot explain usually discover it here, and that gap closes through conversation rather than repetition.

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Covers Probability Alongside Data Analysis

Courses often teach probability and descriptive statistics as separate units, so students rarely practice switching between them. Two problems here check complementary and conditional probability, which is where a shaky grasp of “given that” tends to surface.

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Checks Readiness for the Normal Distribution

The last three problems cover z-scores, the 68–95–99.7 rule, and confidence intervals — the chain that carries into AP Statistics and college coursework. A student who handles all three is ready for formal inference; one who does not now knows exactly where to start.

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Turns One Unit Into a Checklist

A statistics unit covers a lot of unrelated-looking ideas, and it is easy to feel prepared simply because every topic sounds familiar. Answering one question per idea replaces that feeling with a list of what is actually solid.