Descriptive Statistics

The mean is the sum divided by n; the median is the middle value (the average of the two middle values for even n); the mode is the most frequent value, listed only when some value repeats, and all of them when several tie. Variance is the mean squared deviation from the mean: the population form divides by n, the sample form by n − 1 (Bessel's correction, for data that are a sample of something larger — the usual case, and what Excel STDEV.S and most software report by default). Both are shown so you can pick the one your context expects. The standard error of the mean is the sample SD ÷ √n; the coefficient of variation is sample SD ÷ |mean|.

There are at least nine published ways to compute a quartile. This page uses Hyndman & Fan's type 7 — linear interpolation between the sorted values at position (n − 1) × p — which is the default in R, NumPy and Excel's QUARTILE.INC. Other tools (Minitab, some textbooks) use type 6 and will differ slightly on small samples. Outliers are flagged with Tukey's rule: below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. They are flagged, not removed; the summary includes them.

Skewness measures asymmetry (positive = a longer right tail); kurtosis here is excess kurtosis, zero for a normal distribution, positive for heavier tails. Both are the sample-adjusted Fisher–Pearson forms (G1 and G2), the same formulas as Excel's SKEW and KURT and SPSS; NumPy's scipy.stats.skew without the bias correction gives a smaller number. They need at least three and four values respectively and are meaningless for a constant series, where they are left blank.

Numbers may be separated by spaces, line breaks, commas, semicolons or pipes, so a comma is always a separator — write 1234, not 1,234. Currency symbols, percent signs and accounting parentheses are stripped. Anything that is still not a number is listed as ignored rather than dropped silently. Up to 100,000 values; nothing leaves the browser, and the same four anonymous usage counts as the rest of the site apply.