Statistics

Population Variance Calculator

Find the population variance and standard deviation.

Value 1

Value 2

Value 3

Value 4

Value 5

Value 6

Calculated Output

Population variance 2.96

Population SD 1.72

Formula: σ² = Σ(x − μ)² ÷ N

Step-by-Step Breakdown

1. Values used:

2. Value 1 = 4

3. Value 2 = 8

4. Value 3 = 6

5. Value 4 = 5

6. Value 5 = 3

7. Value 6 = 0

9. Population variance = 2.96

10. Population SD = 1.72

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The math behind it

σ² = Σ(x − μ)² ÷ N. It uses N, not N − 1 (which is for samples).

4, 8, 6, 5, 3 → variance 2.8, SD ≈ 1.67.

Population vs sample variance?

Sample variance divides by N − 1 to correct for estimation bias.