Statistics Calculator
Paste a list of numbers to get every common statistic at once: mean, median, mode, standard deviation, variance, quartiles and more.
About the Statistics Calculator
This is a one-stop summary for a data set. The mean and median describe the centre; the standard deviation, variance, range and interquartile range describe the spread; skewness shows whether the tail stretches to the right (positive) or left (negative).
Sample statistics divide by n − 1 (Bessel's correction) to estimate the spread of a larger population from a sample; population statistics divide by n. Quartiles use the same method as Excel's QUARTILE.INC and R's default.
The formula
s = √( Σ(xᵢ − x̄)² ÷ (n − 1) )
- x̄
- mean = Σxᵢ ÷ n
- σ
- population SD: divide by n instead
- SE
- s ÷ √n
Worked example
Example: Mean = 18
- Input: Data: 4, 8, 15, 16, 23, 42.
- Formula: s = √( Σ(xᵢ − x̄)² ÷ (n − 1) )
- Result: Mean = 18
- Count (n): 6
- Sum: 108
- Median: 15.5
Questions people ask
Should I use sample or population standard deviation?
Use the sample value when your data are a subset of a bigger group (most surveys and experiments). Use population only when you have every member.
Why do my quartiles differ from my textbook?
There are several quartile methods. This uses the linear interpolation method of Excel QUARTILE.INC; some textbooks use the median-of-halves method.