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
• w_i: A vector of weights
• x_i: 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:

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