How it works
Compute the population or sample standard deviation, variance, and mean of a list.
Enter a comma-separated list of numbers and choose population or sample. The calculator reports the mean, variance, standard deviation, and count.
Formula
Mean μ = Σx ÷ n; population σ² = Σ(x − μ)² ÷ n; sample s² = Σ(x − μ)² ÷ (n − 1).
xᵢ- Each value (number)
n- Count (count)
Examples
- 2, 4, 4, 4, 5, 5, 7, 9 (population)Values 2, 4, 4, 4, 5, 5, 7, 9 · populationMean 5 · variance 4 · standard deviation 2
Frequently asked questions
Population or sample?
Use sample (n−1) when the list is a sample of a larger group; use population (n) when the list is the entire group.
Why subtract 1 for a sample?
Dividing by n−1 yields an unbiased estimate of the population variance from a sample.
How to read the result
The standard deviation is the typical distance of values from the mean — same units as the data.
Limitations
Univariate only; assumes the data is a simple list of values.
Source: Population and sample variance/standard-deviation definitions.