About Statistics Calculator
Paste numbers separated by commas, spaces or line breaks and every descriptive statistic appears at once. There is no need to decide in advance which measure you want, and seeing them together is often the point — a mean far from the median is itself the finding.
Both the sample and population variants of variance and standard deviation are shown, because the distinction matters and is easy to get wrong. If your numbers are the entire group you care about, use the population figure. If they are a sample you are generalising from, use the sample figure, which divides by n−1 to correct for the fact that a sample underestimates spread.
Outliers are flagged using Tukey's rule — anything more than 1.5 interquartile ranges outside the quartiles. That is the same definition a box plot uses, and it is robust in a way that a standard-deviation-based rule is not, because extreme values inflate the standard deviation they are being measured against.
How to calculate statistics
Paste your numbers
Separated by commas, spaces or line breaks — a column copied from a spreadsheet works directly.
Read the results
Averages, spread, quartiles and outliers all appear at once.
Choose sample or population
Both variance figures are shown; pick the one that matches what your data represents.
Which average should you use?
- Mean — the arithmetic average. Best for symmetric data, but pulled hard by extreme values.
- Median — the middle value. Unaffected by extremes, which is why incomes and house prices are reported as medians.
- Mode — the most frequent value. The only average that works for categories, and the one to use when you care about the most common case.
Sample or population?
Population statistics describe the complete group you care about — every employee, every transaction. Sample statistics describe a subset you are using to estimate something larger.
Sample variance divides by n−1 rather than n. That correction exists because a sample's values cluster around the sample mean rather than the true mean, which makes the raw spread a systematic underestimate.