AP Statistics practice problems: practice problems and exam questions

Practice for AP Statistics: describing data, probability, the normal distribution, regression, confidence intervals, significance tests and chi-square tests.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

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Topics in this course

  1. Descriptive statisticsmean and median · standard deviation · normal distributioncalculations
  2. Probabilityequally likely outcomes · counting and complements · binomial distributioncalculations
  3. Normal distributionarea in one tail · area between two values · percentilescalculations
  4. Linear regression & correlationslope and intercept · correlation coefficient · predictioncalculations
  5. Confidence intervalsz interval · t interval · sample sizecalculations
  6. Hypothesis tests & confidence intervalsz statistic · t statistic · confidence intervalscalculations
  7. Chi-square testsgoodness of fit · test of independence · critical value decisioncalculations

Exam tips for AP Statistics practice problems

  • State the conditions for each inference procedure.
  • Write hypotheses in terms of the population parameter.
  • Interpret every result in the context of the question.

Worked examples

Descriptive statisticsEasy
510152025303540

Find the median M of the data: 39, 11, 3, 28, 18, 17, 40, 40, 5.

n = 9

Find M

Show hints
  1. Sort the values from smallest to largest.
  2. With an odd number of values the median is the middle one.
  3. sorted: 3, 5, 11, 17, 18, 28, 39, 40, 40.
Show the answer and the step-by-step solution

Descriptive statistics: the mean is the sum divided by n; the median is the middle value of the sorted data (the average of the two middle values when n is even). The sample standard deviation is s = √(Σ(x − x̄)²/(n − 1)). A z-score z = (x − μ)/σ says how many standard deviations a value lies from the mean.

Sort

3, 5, 11, 17, 18, 28, 39, 40, 40

Middle value

M = 18

Answer

M = 18
ProbabilityMedium
xp(x)10.1520.3530.0540.350.15μ = 2.95

For the distribution shown, find the variance Var(X) of X.

x: 1, 2, 3, 4, 5p(x): 0.15, 0.35, 0.05, 0.3, 0.15

Find Var(X)

Show hints
  1. μ = Σx·p(x) = 2.95.
  2. Then E(X²) = Σx²·p(x).
  3. Var(X) = E(X²) − μ².
Show the answer and the step-by-step solution

Discrete random variables: a probability distribution lists every value x a variable can take with its probability p(x); the probabilities are between 0 and 1 and add up to 1. The expected value (mean) is E(X) = Σx·p(x), the long-run average. The variance is Var(X) = Σ(x − μ)²·p(x) = E(X²) − μ², and the standard deviation σ = √Var(X). For a linear change Y = aX + b: E(Y) = a·E(X) + b, Var(Y) = a²·Var(X) and σY = |a|·σX; adding a constant does not change the spread.

Mean

μ = 1·0.15 + 2·0.35 + 3·0.05 + 4·0.3 + 5·0.15 = 2.95

Mean of the squares

E(X²) = 1·0.15 + 4·0.35 + 9·0.05 + 16·0.3 + 25·0.15 = 10.55

Variance

Var(X) = 10.55 − 2.95² = 1.848

Answer

Var(X) = 1.848

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Z-score and normal probability calculatorConfidence interval calculatorSample size calculatorMean, median and standard deviation calculatorLinear regression calculatorChi-square goodness-of-fit calculatorNormal distribution calculatorBinomial distribution calculatorPoisson distribution calculatorPermutation and combination calculator (nPr and nCr)t-test calculatorP-value calculatorCorrelation coefficient calculator (Pearson and Spearman)One-way ANOVA calculatorExpected value and variance calculatorSignificant figures calculator (count, round and calculate)Percent error calculator (and percent difference)

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Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.