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Standard Deviation Calculator

Find the mean, variance and standard deviation of a data set.

Std deviation (population) 1.72
Variance 2.96
Mean 5.2

Formula: σ = √( Σ(xᵢ − mean)² ÷ n )

Step-by-step with your numbers:
1. ▶ Data: 4, 8, 6, 5, 3 (n = 5)
2.
3. ▶ Step 1 — Mean (μ): μ = ( 4 + 8 + 6 + 5 + 3 ) ÷ 5 = 5.2
4.
5. ▶ Step 2 — Deviations (xᵢ − μ):
6. x₁ − μ = 4 − 5.2 = -1.2
7. x₂ − μ = 8 − 5.2 = 2.8
8. x₃ − μ = 6 − 5.2 = 0.8
9. x₄ − μ = 5 − 5.2 = -0.2
10. x₅ − μ = 3 − 5.2 = -2.2
11.
12. ▶ Step 3 — Squared deviations (xᵢ − μ)²:
13. (x₁ − μ)² = (-1.2)² = 1.44
14. (x₂ − μ)² = (2.8)² = 7.84
15. (x₃ − μ)² = (0.8)² = 0.64
16. (x₄ − μ)² = (-0.2)² = 0.04
17. (x₅ − μ)² = (-2.2)² = 4.84
18.
19. ▶ Step 4 — Sum of squares Σ(xᵢ − μ)²: 1.44 + 7.84 + 0.64 + 0.04 + 4.84 = 14.8
20.
21. ▶ Step 5 — Variance σ² = Σ(xᵢ − μ)² ÷ n = 14.8 ÷ 5 = 2.96
22.
23. ▶ Step 6 — Standard deviation σ = √(σ²) = √(2.96) = 1.72
Did we solve your problem today?

Standard deviation measures how spread out a set of numbers is around their average. Enter as many values as you'd like, separated by commas or spaces.

The math behind it

Find the mean, then the average of the squared differences from the mean (variance). The standard deviation is the square root of the variance.

Worked example

4, 8, 6, 5, 3 → mean 5.2, variance 2.96, σ ≈ 1.72.

FAQ

Population vs sample SD?

Population divides by n (used here); sample divides by n − 1 for an unbiased estimate from a sample.

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