Weighted Population Standard Deviation and Weighted Population Variance
The formula used for weighted population variance is a straight extension of the population variance. The population variance fomula is:
var_p = sum((xi - µ)2) / N, where µ = sum(xi) / N
The weighted population variance formula is the above with some extension:
wvar_p = sum(wi * (xi - µ')2) / sum(wi), where µ' = sum(wi * xi) / sum(wi)
Example with sample data:
Value |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
23 |
Weight |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
100 |
Mean |
Weighted Mean |
Population Standard Deviation |
Weighted population Standard Deviation |
Population Variance |
Weighted population Variance |
10.75 |
22.08 |
4.99 |
3.50 |
24.94 |
12.25 |