How to use it
- Paste numbers separated by commas, spaces or lines, or switch to a frequency table and enter each value with its count.
- Choose sample (n − 1) or population (n); the result shows the standard deviation, the variance, the mean, the other kind of standard deviation and the coefficient of variation.
- Follow the numbered steps and the table of deviations and squares to check homework or show working; enter a value to get its z-score.
How it calculates
Each number is kept as an exact fraction, so the mean, every deviation and square, the sum of squares and both variances are exact, and only the final square root is rounded. That matters for working shown step by step: ordinary floating-point arithmetic leaves tiny errors (in JavaScript, 0.1 + 0.2 is 0.30000000000000004), which show up as untidy digits in a worked table. For just the mean, median and mode of a list, the Average Calculator is quicker.
What we tested
On October 14, 2026 we compared the page’s own functions with Python’s statistics module working in exact fractions on 3,001 random lists of integers, decimals, negatives and exponent forms: every mean, deviation, square, sum of squares and both variances matched exactly, and both standard deviations to 12 significant figures. Frequency tables expand correctly and bad lines are reported. A version that divided the sample variance by n failed the test. In Chromium: 2, 4, 4, 4, 5, 5, 7, 9 showed a sample standard deviation of 2.138089935 and variance 4.571429… with the steps (sum of squares 32) and an 8-row table; population showed 2 and the z-score of 9 was 2; the same data as a frequency table gave 2; a word in the list showed a message; the page fitted a 390 px phone with no errors.
| 2, 4, 4, 4, 5, 5, 7, 9 | Result |
|---|---|
| Mean | 5 |
| Sum of squares | 32 |
| Population variance and SD | 4 and 2 |
| Sample variance and SD | 32/7 = 4.571428… and 2.138090… |
Frequently Asked Questions
Built by Derek Giordano · Part of Ultimate Design Tools