Statistics math practice
Every calculation the Statistics exam asks for, with new numbers every time. Type the answer rather than picking from four options — producing a number is a different skill from eliminating three wrong ones, and only one of them is what the exam scores.
z-score
A z-score says how many standard deviations a value sits from the mean, which is what makes values from different distributions comparable at all.
A distribution has mean 459.2 and standard deviation 59.2. Calculate the z-score of 509.5.
Every skill in this set
- z-scoreExploring One-Variable Data
- z = (x − μ) / σ
- A z-score says how many standard deviations a value sits from the mean, which is what makes values from different distributions comparable at all.
- Confidence interval margin of errorInference for Quantitative Data: Means
- margin of error = z* × σ/√n
- Quadrupling the sample size only halves the margin of error, because of the square root. That trade-off is a standard free-response discussion point.
- Binomial mean and standard deviationRandom Variables
- μ = np · σ = √(np(1−p))
- Check the binomial conditions before using these: fixed n, two outcomes, constant p, independent trials. A question that violates one is testing whether you noticed.
- Prediction from a regression lineExploring Two-Variable Data
- ŷ = a + bx · residual = observed − predicted
- A residual is observed minus predicted, in that order. A positive residual means the model under-predicted, which is the direction students reverse most often.
Common questions
What math is on the AP Statistics exam?
4 distinct calculations: z-score, confidence interval margin of error, binomial mean and standard deviation, prediction from a regression line. Each one appears on the exam's formula sheet or is assumed by it, so the work is applying the relationship rather than recalling it.
Do the problems repeat?
No. Every problem is generated with fresh numbers, so the same skill can be practiced indefinitely without memorizing an answer. That is the whole point — being able to run a procedure on numbers you have not seen is what the exam actually tests.
How precise does my answer need to be?
Answers are accepted within about 1–3% of the exact value, which allows for rounding at intermediate steps the way a calculator does. Units are optional — type the number and the unit if you like, or just the number.