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The weighted standard deviation is a useful way to measure 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
- 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))
And if you’d like to calculate the weighted variance, it’s simply 8.5702 = 73.44.
Cite this article
stats writer (2025). How to calculate weighted standard deviation in Excel. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/how-to-calculate-weighted-standard-deviation-in-excel/
stats writer. "How to calculate weighted standard deviation in Excel." PSYCHOLOGICAL SCALES, 9 Dec. 2025, https://scales.arabpsychology.com/stats/how-to-calculate-weighted-standard-deviation-in-excel/.
stats writer. "How to calculate weighted standard deviation in Excel." PSYCHOLOGICAL SCALES, 2025. https://scales.arabpsychology.com/stats/how-to-calculate-weighted-standard-deviation-in-excel/.
stats writer (2025) 'How to calculate weighted standard deviation in Excel', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/how-to-calculate-weighted-standard-deviation-in-excel/.
[1] stats writer, "How to calculate weighted standard deviation in Excel," PSYCHOLOGICAL SCALES, vol. X, no. Y, ص Z-Z, December, 2025.
stats writer. How to calculate weighted standard deviation in Excel. PSYCHOLOGICAL SCALES. 2025;vol(issue):pages.