Follow this example. Write the sample data in a column and the corresponding weight for each data point in another column. The weights should add up to 100.
10 = 20
23 = 10
57 =30
75 = 20
92 = 20
Calculate the weighted mean by multiplying each data point by it's corresponding weight. Add each resulting value together and divide by the total weight, which is 100.
Numerator = (10*20)+(23*10)+(57*30)+(75*20)+(92*20)) = 5480
Denominator = 20+10+30+20+20 = 100
Weighted Mean = 5480/100 = 54.8
Calculate the weighted variance by subtracting each data point from the weighted mean. Square this value and multiply by the corresponding weight. Add all of the values together and divide by the total weight.
Numerator =(20*(10-54.8)^2)+(10*(23-54.8)^2)+(30*(57-54.8)^2)+(20*(75-54.8)^2)+(20*(92-54.8)^2) = 86,236
Denominator = 100
Weighted variance = 86,236/100 = 862.36