Descriptive Statistics Calculator
Every summary statistic for a data set at once — centre, spread, shape and the five-number summary.
Three questions describe most data sets: where is the centre, how spread out is it, and is it symmetric.
How the descriptive statistics calculator works
Three questions describe most data sets: where is the centre, how spread out is it, and is it symmetric.
The mean and median answer the first and disagree when the data are skewed — that disagreement is itself informative, which is why both are here. Standard deviation and IQR answer the second, the first sensitive to extremes and the second not. Skewness answers the third: positive means a long right tail, negative a long left one, and anything beyond ±1 is strongly skewed.
The five-number summary — minimum, Q1, median, Q3, maximum — is what a box plot draws.
Formula: mean = Σx/n; s² = Σ(x−x̄)²/(n−1); skew = [n/((n−1)(n−2))] Σ((x−x̄)/s)³
Worked examples
| Inputs | Mean | Note |
|---|---|---|
| Ten measurements | 16.5 | mean 16.5, sd 4.377 |
| A symmetric set | 3 | mean and median both 3 |
| One extreme value pulls the mean | 22 | mean 22, median 3 |
FAQFrequently asked questions
What are descriptive statistics?
Summaries of a data set — its centre, spread and shape — as opposed to inferences about a wider population.
Should I report the mean or the median?
The median when the data are skewed or have outliers; the mean when they are roughly symmetric. Reporting both is often the most honest.
What does skewness tell me?
Which way the tail runs. Positive means a long right tail; beyond about ±1 the data are strongly skewed and the mean is misleading.
What is the standard error?
The standard deviation of the mean itself — how much the sample mean would bounce around if you took the sample again.
What is the five-number summary?
Minimum, Q1, median, Q3, maximum — the five values a box plot draws.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.