Descriptive Statistics Calculator

Mean, median, SD, skewness, kurtosis, percentiles, histogram, density and Q-Q in one click.

Open the Descriptive Statistics calculator

When to use it

Use to summarise a single numeric variable before any inference: mean, median, SD, percentiles, skew, kurtosis. The first step of every analysis pipeline. Reveals outliers, distribution shape, and obvious data-entry errors.

When NOT to use it

Do not use for two-variable comparisons (use t-test or correlation). Do not use for categorical data (use a Frequency or Crosstab tool). Descriptive statistics are not a substitute for a hypothesis test when one is needed.

What you get

Sample size n, mean, median, mode (when unique), variance, sample standard deviation, standard error of the mean, minimum, maximum, range, interquartile range (Q1, Q3), skewness, kurtosis, coefficient of variation; a histogram with overlaid kernel density estimate; a normal Q-Q plot; and a six-panel descriptive panel including a boxplot and reduction summary.

Worked example

Canonical sample-SD worked example (n = 8): mean = 5, sample SD = sqrt(32 / 7).

2, 4, 4, 4, 5, 5, 7, 9

Expected output: mean = 5, sample SD approx 2.13809, median = 4.5

Source: Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods, 8th ed. Iowa State UP, ch. 2 (sec. 2.6, sample variance worked example x = {2, 4, 4, 4, 5, 5, 7, 9}).

How to interpret the output

Mean and median should be close for a symmetric distribution; large divergence indicates skew (mean greater than median for right-skew). Skewness near zero and kurtosis near three are normal-like; |skewness| > 1 or kurtosis > 5 are flags for non-normality. Standard error tells you the precision of the mean estimate (CI = mean +/- 1.96 SE for large n). Sample SD uses n-1 (Bessel correction). Cross-checked against the canonical sample-SD worked example x = {2, 4, 4, 4, 5, 5, 7, 9} (Snedecor and Cochran 1989 ch. 2) to four significant figures.

Common pitfalls

Reporting the mean without the SD or SE alongside it.
Confusing population SD (divide by n) with sample SD (divide by n-1).
Reading skewness or kurtosis as proof of non-normality without a Q-Q plot or formal test.
Treating a histogram with few bins as evidence about the underlying distribution shape.

Try it in StatVeda

The Descriptive Statistics engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.

Open Descriptive Statistics

References

Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley, Reading, Massachusetts.
Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods, 8th edition. Iowa State University Press, Ames. Chapters 1 and 2.