Variance Calculator

Find population and sample variance.

Population variance 200

Sample variance 250

Mean 30

Formula: σ² = Σ(x−mean)² ÷ n ; s² uses n−1

Step-by-step with your numbers:

1. ▶ Data: 10, 20, 30, 40, 50 (n = 5)

3. ▶ Step 1 — Mean (μ): μ = ( 10 + 20 + 30 + 40 + 50 ) ÷ 5 = 30

5. ▶ Step 2 — Deviations (xᵢ − μ):

6. x₁ − μ = 10 − 30 = -20

7. x₂ − μ = 20 − 30 = -10

8. x₃ − μ = 30 − 30 = 0

9. x₄ − μ = 40 − 30 = 10

10. x₅ − μ = 50 − 30 = 20

11.

12. ▶ Step 3 — Squared deviations (xᵢ − μ)²:

13. (x₁ − μ)² = (-20)² = 400

14. (x₂ − μ)² = (-10)² = 100

15. (x₃ − μ)² = (0)² = 0

16. (x₄ − μ)² = (10)² = 100

17. (x₅ − μ)² = (20)² = 400

18.

19. ▶ Step 4 — Sum of squares Σ(xᵢ − μ)²: 400 + 100 + 0 + 100 + 400 = 1000

20.

21. ▶ Step 5 — Population variance σ² = Σ(xᵢ − μ)² ÷ n = 1000 ÷ 5 = 200

22. ▶ Sample variance s² = Σ(xᵢ − μ)² ÷ (n − 1) = 1000 ÷ 4 = 250

Did we solve your problem today?

Variance measures how spread out your data is (the square of standard deviation).

The math behind it

Average of squared deviations from the mean. Population divides by n; sample divides by n−1.

10,20,30,40,50 → population variance 200.

Population or sample?

Use sample (n−1) when your data is a sample of a larger group.