What this calculator does
Chebyshev’s theorem works out minimum share of any data set within k standard deviations of the mean, whatever its shape. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
The inputs explained
| Field | What to enter |
|---|---|
| Number of standard deviations (k) | A number. Starts at 2. |
| Mean (optional, for the interval) | A number. Starts at 100. |
| Standard deviation (optional, for the interval) | A number. Starts at 15. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with number of standard deviations (k)
Every other input is held at the calculator’s starting values while number of standard deviations (k) varies. Select any row to load that scenario into the calculator.