Quick Statistics

Mean, standard deviation, median and more — 100% local.

Results

Box plot

Calculation performed entirely in your browser. The "population" variance and standard deviation divide by n, the "sample" version (used to estimate a population from a sample) divides by n−1.

Mean or median?

The mean adds up all the values and divides by their count. The median is the middle value once the series is sorted. The difference matters as soon as there are extreme values: for the salaries 3000, 3200, 3500, 3800, 40000, the mean is 10,700 — a figure no one earns — while the median, 3500, describes the centre of the group well. The median resists outliers; the mean does not.

Standard deviation: population or sample?

Standard deviation measures the spread around the mean. Two formulas coexist depending on what your series represents.

population: σ = √(Σ(xᵢ − x̄)² / n)
sample: s = √(Σ(xᵢ − x̄)² / (n − 1))

Divide by n if your series is the whole population studied (the marks of this class). Divide by n − 1 if it's only a sample meant to represent a larger whole (a survey). The "−1" corrects a bias: a sample naturally underestimates the true spread.

Quartiles and box plot

The quartiles Q1, Q2 (the median) and Q3 cut the sorted series into four equal parts. The box runs from Q1 to Q3 and therefore holds the central half of the data; its width (Q3 − Q1) is the interquartile range. The whiskers stretch to the values still considered "normal", and points beyond them are flagged as outliers.

Remember: a single statistic never describes a series. Always look together at a measure of centre (mean, median) and a measure of spread (standard deviation, interquartile range).

Frequently asked questions

Which separators are accepted?

Spaces, commas, semicolons and line breaks, freely mixed. The decimal separator is the point.

Is my data transmitted?

No. Everything is computed locally; the series you enter doesn't leave the browser and disappears when the tab is closed.

How is the median computed for an even number of values?

It's the average of the two central values of the sorted series.