Statistics Calculator (Mean, Median, Mode, SD)
Compute mean, median, mode, standard deviation, variance, and quartiles from a dataset.
Formula
σ = √( Σ(xᵢ − μ)² / N ) · s = √( Σ(xᵢ − x̄)² / (N−1) )
Tips
- Use the sample standard deviation (n−1) when your data is a sample drawn from a larger population — this is the usual case.
- The median resists outliers; the mean does not. A large gap between them signals a skewed distribution.
- The IQR is a robust spread measure. Points beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR are conventional outliers.
Frequently asked questions
Why are there two standard deviations?
Dividing by N gives the population standard deviation, correct when your data is the entire population. Dividing by N−1 (Bessel’s correction) gives an unbiased estimate when your data is a sample.