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Statistics · Data summaries

Descriptive Statistics Calculator

Summarize a dataset with count, mean, median, mode, range, population or sample variance, and standard deviation using explained definitions.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

An unweighted list treated as a population or a sample

Arithmetic mean

Population: μ = Σxᵢ/nSample: x̄ = Σxᵢ/n

Population spread

σ² = Σ(xᵢ−μ)²/nσ = √σ²

Sample spread

s² = Σ(xᵢ−x̄)²/(n−1)
Descriptive statistics

Summarize a numerical dataset

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

x̄ = Σxᵢ / n

Paste at least two values separated by commas, spaces, or semicolons.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Data are treated as an unweighted numerical list. Population variance divides by n; sample variance uses the Bessel-corrected denominator n − 1. The tool reports no unique mode when every value occurs once.

Worked examples

See the method in practice

01

Repeated central value

For 1, 2, 2, 3, the mean and median are 2 and the mode is 2.

02

Sample variance

For the sample 1, 2, 3, the mean is 2 and the sample variance is 1.

Questions

Frequently asked

Should I choose sample or population?

Choose population when the entered values are the entire group of interest; choose sample when they estimate a larger population.

Can a dataset have several modes?

Yes. Every value tied for the greatest frequency is reported.

Are units preserved?

Mean, median, range, and standard deviation use the original unit; variance uses its square.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

NIST/SEMATECH e-Handbook — Measures of Location

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology