Statistics practice problems that never repeat
Most statistics practice sets have a fixed list of problems and the answers at the back. You work through them once, remember that the standard deviation question comes out to 5.35, and the second time through you are recalling, not calculating. Statisticsdrill was built around one rule: every attempt gets a fresh sample, so the only way through a problem is the method.
Each of the 53 problem types is a template. Every attempt generates new data or a new scenario: a new set of ticket times, a new survey share, a new pair of conversion rates. Press New numbers and you get another version whenever you like. That is the difference between recognizing a formula and being able to use it in an exam or a report.
Statistics exercises with answers, worked step by step
There is nothing to install. Each problem states the scenario and how to round, you enter one number, and for hypothesis tests you also choose reject or fail to reject. Both parts are checked. When an answer is off, the checker names the likely mistake: population instead of sample standard deviation, one tail instead of two, z instead of t, or the wrong rounding.
Every worked solution shows the formula with the numbers filled in, the steps, and the matching Excel or Google Sheets function, such as STDEV.S, NORM.DIST, T.DIST.2T, CHISQ.DIST.RT or SLOPE. Show the data opens the generated sample as a table, with a histogram, a scatter plot or a shaded normal curve where it helps.
Business statistics practice built in five levels
The 53 problem types are organized into levels, and each level only adds one or two ideas on top of what you already know.
- Describing data: mean, median, mode and range, sample and population standard deviation, the z-score of one value, percentiles by the inclusive method, coefficient of variation, weighted mean.
- Probability: at least one by the complement, the addition and multiplication rules, conditional probability from a two-way table, Bayes for a positive screening result, total probability, expected value of a raffle ticket, permutations, combinations and sampling without replacement.
- Distributions: binomial exactly k and at least k with its standard deviation, Poisson exactly k and at most k, normal areas between and above values, percentile cutoffs, the sampling distribution of the mean and the normal approximation to the binomial.
- Inference: critical t values, margin of error, confidence intervals for a mean and a proportion, sample size for each, one-sample, two-sided, one-sided and paired t tests with p-values, two-proportion z tests and chi-square tests of independence.
- Relationships: correlation coefficient, regression slope and intercept, predicted values, residuals, R squared, reading a slope in units, and the lift and significance of an A/B test.
Within a level the problems get harder one notch at a time. By the end of Inference you have chosen between z and t, between one tail and two, computed the p-value and made the decision, not because you read about it, but because the problem would not pass until you did.
Open the problem list
Hypothesis testing practice, decision included
Hypothesis tests are where most statistics marks are lost, because a correct statistic with the wrong decision is still wrong. Statisticsdrill checks both: the number you compute and whether you reject or fail to reject at the stated significance level.
The Inference level covers the tests that show up in business and social science courses and in real reports: one-sample t tests with two-sided and one-sided alternatives, paired t tests, two-proportion z tests for conversion rates, and chi-square tests of independence on two-way tables. Each comes with fresh data every time, so the decision has to be reasoned, not remembered.
Probability practice problems with real scenarios
The Probability level uses the situations that appear in exams and at work: the chance that at least one of several shipments is late, the probability a customer is both returning and from one region, the chance someone with a positive screening result actually has the condition, the expected value of a ticket, the number of ways to pick a committee.
Bayes and conditional probability get their own problems with fresh numbers, because they are the two that most people can follow in a textbook and still cannot start from scratch.
Learn statistics by getting it wrong first
A hint is one click away, but the worked answer opens only after your second attempt. That is on purpose. Entering a number, seeing it marked off, reading that you used the population formula instead of the sample one, and fixing it yourself is the part that sticks. Copying a solution before you have tried does not.
Every problem also explains the idea behind it: why the sample standard deviation divides by n minus 1, why the standard error shrinks with the square root of n, why a one-sided test has a smaller p-value than a two-sided one on the same data.
Statistics exam practice and timed problems
Introductory statistics courses, business analytics programs, the CFA Level I quantitative section and data analyst assessments all test this material under time pressure. Statisticsdrill's timed mode puts a clock on each problem with hints and answers locked until time is up, and fresh numbers mean you cannot coast on a remembered result.
Run through the first four levels in the week before an exam, with New numbers for the types that give you trouble, and the questions will feel like problems you have already done.
Try a timed problem
Statistics in Excel and Google Sheets, function by function
Most working analysts do their statistics in a spreadsheet, so every worked solution ends with the function that does the same thing: AVERAGE, MEDIAN, STDEV.S and STDEV.P, PERCENTILE.INC, BINOM.DIST, POISSON.DIST, NORM.DIST and NORM.INV, CONFIDENCE.T, T.TEST, CHISQ.TEST, CORREL, SLOPE, INTERCEPT and FORECAST.LINEAR.
Seeing the formula and the function side by side is the fastest way to trust the spreadsheet result, and the fastest way to notice when a function uses a different convention than your course.
Statistics practice for students and working analysts
If you have never computed a standard deviation, Describing data starts with the mean and does not assume anything. If you already run A/B tests, skip to Inference or Relationships and look for the gaps: most analysts have one test they have always run through software without being sure what it does, and fresh numbers find it quickly.
Every problem type is independent, so you can jump to the one you need for today's report and come back to the rest later.
Statisticsdrill