Statistics Calculator (mean / median / mode / stddev / variance)

All 5 descriptive statistics from a list of numbers — sample + population variants for std dev / variance.

Result

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General calculation reads

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How Not to Be Wrong

Jordan Ellenberg - math thinking

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The Joy of X

Steven Strogatz - accessible math

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Scientific calculator (Casio fx-991EX)

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How to use this calculator

Paste your numbers — comma-separated, space-separated, or one-per-line all work.
Non-numeric tokens are silently skipped (so pasting from a table with labels won't break it).
Read mean / median / mode side-by-side. For descriptive stats use SAMPLE variants by default.

About this calculator

Five descriptive statistics in one tool, plus quartiles + IQR + range + coefficient of variation. Mean is the arithmetic average Σx/n. Median is the middle value (or the average of the two middle values for even n) — robust to outliers in ways the mean is not. Mode is the most frequent value; reported as "no mode" if all values are unique. Standard deviation and variance come in TWO flavors: sample (n−1 denominator, Bessel's correction — the unbiased estimator when your data is a sample drawn from a larger population) and population (n denominator — when your data IS the entire population). Use sample by default — almost all real-world datasets are samples. The coefficient of variation (std dev / mean × 100) is a dimensionless relative-spread measure, useful for comparing variability across datasets with different units.

Frequently asked

Sample vs population — which one?+

Default to SAMPLE when your data is a measured subset of a larger population (almost always in real-world data analysis). Use POPULATION when your data is the entire population of interest (e.g. grades for ALL students in one class).

Why is the n−1 denominator the "right" one for sample variance?+

Bessel's correction. The n denominator is biased — it systematically underestimates the population variance because the sample mean is "closer" to the data than the (unknown) population mean. Dividing by n−1 corrects the bias and yields an unbiased estimator.

When is the mode useful?+

For categorical or discrete data (test scores, dice rolls, customer-segment counts). For continuous data the mode is usually unique (no repetition) and uninformative — use mean/median instead.

Q1 / Q3 calculation method?+

This tool uses the simple "median-of-halves" method: Q1 = median of the lower half. Other methods (NIST, Tukey, Excel's QUARTILE.INC vs QUARTILE.EXC) differ by ~1 position; for n > 50 they converge.

Source?+

Stigler SM (1986) "The History of Statistics" — Bessel's correction history. Tukey JW (1977) "Exploratory Data Analysis" — five-number summary + IQR. Modern reference: Wasserman L (2004) "All of Statistics" Ch. 6.