How to Calculate Weighted Standard Deviation in Excel


The weighted standard deviation is a useful way to measure the dispersion of values in a dataset when some values in the dataset have higher weights than others.

The formula to calculate a weighted standard deviation is:

where:

  • N: The total number of observations
  • M: The number of non-zero weights
  • wi: A vector of weights
  • xi: A vector of data values
  • x: The weighted mean

The following step-by-step example shows how to calculate a weighted standard deviation in Excel.

Step 1: Create the Data

First, let’s create a column of data values along with their weights:

Step 2: Calculate the Weighted Mean

Next, we can use the following formula to calculate the weighted mean:

=SUMPRODUCT(A2:A11, B2:B11) / SUM(B2:B11)

The weighted mean turns out to be 31.147:

Step 3: Calculate the Weighted Standard Deviation 

Next, we can use the following formula to calculate the weighted standard deviation:

=SQRT(SUMPRODUCT((A2:A11-E2)^2, B2:B11) / SUM(B2:B11, -1))

The weighted standard deviation turns out to be 8.570:

Weighted standard deviation formula in Excel

And if you’d like to calculate the weighted variance, it’s simply 8.5702 = 73.44.

Additional Resources

How to Calculate Weighted MAPE in Excel
How to Find Weighted Moving Averages in Excel

5 Replies to “How to Calculate Weighted Standard Deviation in Excel”

  1. The excel formula in step 3 is incorrect. Specifically, the denominator (SUM(B2:B11, -1)) in the SQRT is off. While SUM(B2:B11) adds up the weights, that sum is supposed to be multiplied by (M-1)/M, not reduced by 1.

  2. Hi Zach, I don’t understand your weighted standard deviation formula in Excel. Should you not also consider the number of the weights (M and M-1)? Thanks for the clarification.
    !

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