PEAZIT Aha card
Go straight to resources ↓Variance measures spread around the mean
Subtract the mean from each value, square each difference and average these squares. Opposite deviations can no longer cancel.
| Relation | Meaning |
|---|---|
| x̄ = (1 + 3 + 5)/3 = 3 | First calculate the dataset's center. |
| (1 − 3)² + (3 − 3)² + (5 − 3)² = 8 | Squared deviations are 4, 0 and 4. |
| σ² = 8/3 | Divide by all three observations. |
One worked example
- x̄ = (1 + 3 + 5)/3 = 3First calculate the dataset's center.
- (1 − 3)² + (3 − 3)² + (5 − 3)² = 8Squared deviations are 4, 0 and 4.
- σ² = 8/3Divide by all three observations.
Watch out: Here we divide by n for the complete described population. A sample variance estimator often uses n−1. Standard deviation is the square root of variance.
Goal, prerequisites and card origin
What you will learn: Calculate variance for the complete described population.
What you need first: Arithmetic mean and squaring.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Subtract the mean from each value, square each difference and average these squares. Opposite deviations can no longer cancel.