StatisticsdrillStatistics practice problems, from descriptive statistics to regression
Working problems is the only reliable way to get a statistics exam, a data-analyst screening or a research methods course under control. This page lists the problems on Statisticsdrill by topic, in the order a course covers them, so you can go straight to the one you are stuck on. Each problem checks your number as you type it and shows the full working once you have tried.
Descriptive statistics problems
Mean, median, mode and range are quick, but sample versus population standard deviation and the coefficient of variation are where marks are lost. The weighted mean problem is the one that shows up in grading schemes and portfolio returns.
Probability problems
The probability rules, conditional probability, counting and the binomial, Poisson and normal distributions have their own page with every problem listed: the probability practice problems page. The ones most often asked in interviews are below.
Confidence interval problems
A confidence interval is an estimate plus or minus a margin of error. The two decisions are which critical value to use (t for a mean with an unknown population standard deviation, z for a proportion) and how to turn a required margin into a sample size.
Hypothesis testing problems
Every test follows the same route: a test statistic, a p-value or a critical value, a decision. The problems cover the one-sample t-test, one- and two-tailed p-values, the two-proportion z-test and the paired t-test, which is the one people run as an independent test by mistake.
Chi-square problems
The chi-square test of independence compares observed counts with the counts you would expect if two variables were unrelated. The arithmetic is simple but long, so the problems come with the expected-count step shown in the solution.
Correlation and regression problems
Correlation measures how tightly points sit on a line; regression gives the line. The problems go from computing r and the slope by hand to predicting a value, reading a residual, interpreting R-squared and testing whether a correlation is significant.
A/B testing problems
Product and marketing analysts get asked these in interviews: compute the lift between two conversion rates, then decide whether the difference is statistically significant with a two-proportion test.
Start with the free problems
Five problems are free without an account. Pro unlocks all 55, with worked solutions, a diagnosis of common mistakes and progress saved to your account, for $12 a month or $79 once.
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Which courses do these problems cover?
A first statistics course: AP Statistics, Statistics 101 or an introductory business, psychology or nursing statistics class, plus the questions asked in data-analyst and product-analyst interviews.
Are the solutions worked step by step?
Yes. Each problem shows the formula, the substituted numbers and the result after you have tried it twice, or immediately once solved.
Can I use these to prepare for an exam?
Timed mode puts a clock on each problem and keeps hints and solutions closed until it runs out, which is the closest thing to exam conditions.
Do I need software?
No. A calculator is enough for every problem. Where a table or a spreadsheet function would normally be used, the solution names it.