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 | Weight |
| 6 | 1 |
| 7 | 1 |
| 8 | 1 |
| 9 | 1 |
| 10 | 1 |
| 11 | 1 |
| 12 | 1 |
| 13 | 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 |
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