Altair® Panopticon

 

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