Statistics Calculators

Descriptive statistics summarize a data set with a few numbers: where its center is and how spread out it is. These calculators compute those summaries and show the sorted data, sums and deviations behind them.

Calculators

Standard Deviation Calculator

Paste a data set to get the standard deviation, variance and mean, with the full table of deviations.

Confidence Interval Calculator

Enter a sample mean and standard deviation, or a count of successes, with the sample size and a confidence level such as 95. Get the interval, the margin of error and every step, including the exact t critical value for your degrees of freedom.

Linear Regression Calculator

Paste your x values and matching y values. Get the least-squares regression line with an exact slope and intercept, the correlation coefficient r, the coefficient of determination r², and a predicted y for any x you choose.

Mean Median Mode Calculator

Four measures of a data set from one list of numbers, with the sorting and counting shown.

Probability Calculator

Find the probability of a single event, of two independent events, of A given B, or of k successes in n trials, with exact fractions and every step shown.

Permutation and Combination Calculator

Count arrangements and selections with nPr, nCr, permutations with repetition and combinations with repetition, using exact arithmetic and clear factorial steps.

Z-Score Calculator

Standardize a value, find the area to the left, right or between z-scores, or turn a percentile back into a z-score, with each step of the normal-curve calculation shown.

Topics covered

Measures of center: Mean, median and mode, and when each is appropriate.
Measures of spread: Range, variance and sample versus population standard deviation.
Probability and counting: Event probabilities, permutations and combinations.
Standard scores: Z-scores and areas under the normal curve.

Working with data sets

Paste or type your data separated by commas, spaces or new lines. The calculators sort the values, count them and show every intermediate total, so you can see how the mean, median and mode are found and why they differ when a data set is skewed. Standard deviation is shown for both a sample and a population, because the two formulas divide by different numbers and give different answers.

For probability and counting, the calculators explain whether order matters and whether items can repeat, which decides between permutations, combinations and the basic counting principle. Z-scores are converted to areas under the normal curve with a clear statement of which tail is being measured.

Choosing the right summary

Always report a measure of center together with a measure of spread. Two classes can share a mean score of $70$ while one has every score between $65$ and $75$ and the other ranges from $40$ to $100$ ; the standard deviation is what tells them apart.

The mean uses every value but is pulled by outliers, while the median describes the typical value of skewed data such as incomes or house prices. The range is quick to compute but depends on two values only, whereas the standard deviation measures how far a typical value is from the mean. Reporting a center together with a spread, for example the median with the interquartile range, gives a much fairer picture of a data set than a single number.

Courses and topics

Topic explainers with worked examples, common mistakes and practice questions in Statistics.

Introductory Statistics

High school · 3 topic explainers

Descriptive statistics through inference.

Guides

Mean, Median, Mode and Standard Deviation: A Complete Guide
Mean, median and mode describe the centre of a data set, while range and standard deviation describe how spread out it is. Knowing how to compute each one, and when each gives an honest summary, is the foundation of statistics.