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Calculating the weighted standard deviation in Excel involves using a mathematical formula to determine the measure of dispersion for a set of data, taking into account the importance or weight of each data point. This is useful in situations where certain data points hold more significance or influence over the overall data set. Excel provides a built-in function, the “STDEV.S” function, which can be used to calculate the weighted standard deviation by inputting the data set and corresponding weights. This allows for a more accurate representation of the variability of the data. By using the appropriate formula and Excel’s built-in function, one can easily calculate the weighted standard deviation and gain valuable insights into the distribution of the data.
Calculate Weighted Standard Deviation in Excel
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.