Statistics calculator
Mean, median, mode, standard deviation, quartiles and outliers from a list of numbers.
How it works
Paste a list of numbers and get the full summary: mean, median, mode, range, variance, standard deviation, quartiles and interquartile range.
Sample and population standard deviation are both reported, and the difference matters. The sample version divides by n − 1 rather than n, which corrects a bias — using the sample mean rather than the true mean makes deviations systematically too small. Unless you have measured every member of the population, the sample figure is the one you want.
Median and mean diverge whenever the data is skewed, and the gap between them is itself informative. Income is the standard example: a handful of very large values pull the mean well above the median, which is why median income is the more representative figure.
Outliers are flagged by the 1.5 × IQR rule, which is a convention rather than a law. A flagged point is worth looking at, not automatically worth deleting.
This tool runs entirely in your browser. Nothing you enter is sent to a server, logged or stored, and the page keeps working with the network disconnected.
Common questions
- Should I use sample or population standard deviation?
- Sample, unless you have measured the entire population. Dividing by n − 1 corrects the bias introduced by using the sample mean.
- When is the median better than the mean?
- Whenever the data is skewed or has outliers. Income is the classic case — a few very high values pull the mean away from what a typical person earns.
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Sources
- Calculated on this page — At One Place