How to use this calculator
- Enter or paste your numbers, separated by commas, spaces or line breaks. You can copy a column straight from a spreadsheet.
- Use a dot as the decimal separator inside lists.
- Results update as you type; the sorted data table can be downloaded as CSV.
Formula
Quartiles use linear interpolation between sorted values (the same method as Excel's QUARTILE.INC and R's default). Sample variance divides by n − 1; population variance by n.
Mean x̄ = Σx / n
Sample variance s² = Σ(x − x̄)² / (n − 1)
Qp = x₍ₖ₎ + h(x₍ₖ₊₁₎ − x₍ₖ₎), with (n − 1)p = k + h
IQR = Q3 − Q1
Example
- Data: 12, 15, 11, 18, 15, 20, 14, 15, 17, 13 (n = 10).
- Sum = 150, mean = 15, median = 15, mode = 15 (three times).
- Range = 20 − 11 = 9.
Frequently asked questions
Should I use sample or population standard deviation?
Use the sample version when your data is a sample from a larger group (the usual case). Use the population version only when you have data for every member of the group.
Why do different tools give different quartiles?
There are at least nine standard ways to compute quartiles. Results differ slightly for small data sets. This tool uses the common linear interpolation method.
What does skewness mean?
Skewness measures asymmetry. Positive values mean a longer right tail (a few large values), negative values a longer left tail, and values near 0 a roughly symmetric distribution.