How to use this calculator
Type or paste the data. Results, the histogram and the box plot update as you type. Choose the quartile method your course uses; the others differ slightly for small samples.
Formulas
Meanx̄ = Σx/n
Sample variances² = Σ(x − x̄)²/(n − 1)
Population varianceσ² = Σ(x − x̄)²/n
Outliersbelow Q₁ − 1.5 IQR or above Q₃ + 1.5 IQR
Worked example
Fifteen tensile strengths in MPa (the default)
- Σx = 6081, so x̄ = 405.4 MPa; the median (8th value) is 405.
- Σ(x − x̄)² = 1203.6, s² = 85.97, s = 9.27 MPa.
- Q₁ = 398 and Q₃ = 412 by the (n + 1)p rule; IQR = 14, no outliers.
Frequently asked questions
Sample or population standard deviation?
Use s (divide by n − 1) when the data are a sample used to estimate a larger population, which is almost always the case in engineering.
Why do calculators disagree on quartiles?
There are several accepted definitions. They agree for large samples but can differ for small ones.