Mathematics · Grades 10–12
Population variance
This is population variance: divide by N, not N − 1.
The key idea
This is population variance: divide by N, not N − 1.
σ² = Σ(x − μ)²/N
Worked examples
Find the population variance of 1, 10, 19, 28, 37. Divide by 5.
μ = 19; (324 + 81 + 0 + 81 + 324)/5 = 162
162
Find the population variance of 46, 52, 58, 64, 70. Divide by 5.
μ = 58; (144 + 36 + 0 + 36 + 144)/5 = 72
72
Try it yourself
Find the population variance of 3, 7, 11, 15, 19. Divide by 5.
Find the population variance of 14, 20, 26, 32, 38. Divide by 5.
Check your understanding
Answers and marking notes
- 32
μ = 11; (64 + 16 + 0 + 16 + 64)/5 = 32
- 72
μ = 26; (144 + 36 + 0 + 36 + 144)/5 = 72
Further reading and review references
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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.