PEAZIT Aha card
Go straight to resources ↓A weighted mean gives some values more votes
Multiply each value by its weight, add the products and divide by the sum of weights. A weight can count repeated observations.
| Relation | Meaning |
|---|---|
| x̄ = (w₁x₁ + w₂x₂)/(w₁ + w₂) | The denominator is the sum of weights. |
| x₁ = 2; w₁ = 1; x₂ = 4; w₂ = 3 | Four contributes three times as strongly as two. |
| x̄ = (2 + 12)/4 = 3.5 | The list 2, 4, 4, 4 gives the same mean. |
One worked example
- x̄ = (w₁x₁ + w₂x₂)/(w₁ + w₂)The denominator is the sum of weights.
- x₁ = 2; w₁ = 1; x₂ = 4; w₂ = 3Four contributes three times as strongly as two.
- x̄ = (2 + 12)/4 = 3.5The list 2, 4, 4, 4 gives the same mean.
Watch out: Here weights are nonnegative and their sum is positive. Weight group means by group sizes, not by the number of groups.
Goal, prerequisites and card origin
What you will learn: Calculate an average with unequal weights.
What you need first: Arithmetic mean and multiplication.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Multiply each value by its weight, add the products and divide by the sum of weights. A weight can count repeated observations.