About the standard deviation calculator
Standard deviation measures how spread out numbers are around their average. A small value means the numbers cluster near the mean; a large value means they are scattered.
Choose Population if your list contains every value you care about, and Sample if it is only a part of a larger group. The sample version divides by n − 1 instead of n, which corrects for the fact that a sample tends to underestimate the spread of the whole group.
The result also shows the count, sum, mean, variance, the sum of squared deviations and the standard error of the mean, which tells you how precisely the mean is estimated.
Formula
- Mean: x̄ = Σx ÷ n
- Population: σ = √(Σ(x − x̄)² ÷ n)
- Sample: s = √(Σ(x − x̄)² ÷ (n − 1))
- Standard error = s ÷ √n
Example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared deviations add up to 32. The population variance is 32 ÷ 8 = 4, so σ = 2. The sample variance is 32 ÷ 7 = 4.571, so s ≈ 2.138.