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**A vector of weights_{i}:**x**A vector of data values_{i}:**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 8.570^{2} = **73.44**.

**Additional Resources**

How to Calculate Weighted MAPE in Excel

How to Find Weighted Moving Averages in Excel

i wanna ask, what is the (-1) at the last part of the formula for?

i wanna ask, what is the (-1) at the last part of the formula for?

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.

Brilliant blogs!

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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