Averages, standard deviation, z-scores, normal distributions and probability calculations. Use the calculators for your own numbers and the guides for formulas, examples and common questions.
Use the tool that matches the exact problem you need to solve.
Calculate mean, variance and standard deviation for a sample or an entire population.
Find the mean, median, mode and range of a list of numbers.
Find the arithmetic mean of a comma-separated list of numbers.
Calculate a z-score from a value, mean and standard deviation.
Find the cumulative probability below, above or between values in a normal distribution.
Calculate the probability of one event, its complement, and simple independent AND/OR combinations.
Calculate combinations nCr: the number of ways to choose r items from n when order does not matter.
Calculate permutations nPr: the number of ordered arrangements of r items chosen from n.
Three long-tail answers that explain formulas and common scenarios behind this calculator cluster.
Learn what standard deviation measures, how population and sample standard deviation differ, and how to calculate variance and standard deviation step by step.
Read guide →Statistics & ProbabilityLearn the difference between mean, median and mode and when each measure of center is most useful.
Read guide →Statistics & ProbabilityLearn the z-score formula and how to interpret distance from the mean in standard-deviation units.
Read guide →Averages, standard deviation, z-scores, normal distributions and probability calculations. The pages in this cluster are intentionally connected: calculator pages handle the arithmetic, while the guides answer informational searches, show worked examples and explain how to interpret the result.
Use the examples as reference points, then open a calculator and substitute your own values. For decisions involving contracts, taxes, health, payroll rules, construction requirements or other high-stakes details, verify the real-world assumptions with an appropriate authoritative source.
Continue into another connected area of the reference library.