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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 easiest way to calculate a weighted standard deviation in R is to use the wt.var() function from the Hmisc package, which uses the following syntax:
#define data values x <- c(4, 7, 12, 13, ...) #define weights wt <- c(.5, 1, 2, 2, ...) #calculate weighted variance weighted_var <- wtd.var(x, wt) #calculate weighted standard deviation weighted_sd <- sqrt(weighted_var)
The following examples show how to use this function in practice.
Example 1: Weighted Standard Deviation for One Vector
The following code shows how to calculate the weighted standard deviation for a single vector in R:
library(Hmisc) #define data values x <- c(14, 19, 22, 25, 29, 31, 31, 38, 40, 41) #define weights wt <- c(1, 1, 1.5, 2, 2, 1.5, 1, 2, 3, 2) #calculate weighted variance weighted_var <- wtd.var(x, wt) #calculate weighted standard deviation sqrt(weighted_var) [1] 8.570051
The weighted standard deviation turns out to be 8.57.
Example 2: Weighted Standard Deviation for One Column of Data Frame
The following code shows how to calculate the weighted standard deviation for one column of a data frame in R:
library(Hmisc) #define data frame df <- data.frame(team=c('A', 'A', 'A', 'A', 'A', 'B', 'B', 'C'), wins=c(2, 9, 11, 12, 15, 17, 18, 19), points=c(1, 2, 2, 2, 3, 3, 3, 3)) #define weights wt <- c(1, 1, 1.5, 2, 2, 1.5, 1, 2) #calculate weighted standard deviation of points sqrt(wtd.var(df$points, wt)) [1] 0.6727938
The weighted standard deviation for the points column turns out to be 0.673.
Example 3: Weighted Standard Deviation for Multiple Columns of Data Frame
library(Hmisc) #define data frame df <- data.frame(team=c('A', 'A', 'A', 'A', 'A', 'B', 'B', 'C'), wins=c(2, 9, 11, 12, 15, 17, 18, 19), points=c(1, 2, 2, 2, 3, 3, 3, 3)) #define weights wt <- c(1, 1, 1.5, 2, 2, 1.5, 1, 2) #calculate weighted standard deviation of points and wins sapply(df[c('wins', 'points')], function(x) sqrt(wtd.var(x, wt))) wins points 4.9535723 0.6727938
The weighted standard deviation for the wins column is 4.954 and the weighted standard deviation for the points column is 0.673.