Weighted Mean in R (5 Examples)

 

This tutorial explains how to compute the weighted mean in the R programming language.

The tutorial is mainly based on the weighted.mean() function. So let’s have a look at the basic R syntax and the definition of the weighted.mean function first:

 

Basic R Syntax of weighted.mean():

weighted.mean(x, weights)

 

Definition of weighted.mean():

The weighted.mean function computes the weighted arithmetic mean of a numeric input vector.

 

This article contains five examples including reproducible R codes.

You are here for the answer, so let’s move on to the examples!

 

Example 1: Basic Application of weighted.mean Function in R

First, we need to create some example data and a vector with corresponding weights. Consider the following example data:

x1 <- c(9, 5, 2, 7, 3, 6, 4, 5)                    # Create example data
w1 <- c(2, 3, 1, 5, 7, 1, 3, 7)                    # Create example weights

Now, we can use the weighted.mean command to compute the weighted mean of this data:

weighted.mean(x1, w1)                              # Apply weighted.mean function
# 4.965517

As you can see based on the RStudio console output, the weighted mean of our data is 4.965517.

 

Example 2: Handle NAs with weighted.mean Function

A typical problem is the occurrence of missing values in our data (i.e. NA values). Let’s extent our example data with NA values to simulate this situation:

x2 <- c(x1, NA)                                    # Create vector with NA
w2 <- c(w1, 3)                                     # Extend weights vector

If we now apply the weighted.mean function as in Example 1, the RStudio console returns NA:

weighted.mean(x2, w2)                              # weighted.mean with NA
# NA

Fortunately, we can easily ignore NA values in our data with the na.rm option of the weighted.mean function:

weighted.mean(x2, w2, na.rm = TRUE)                # Remove missing values
# 4.965517

 

Example 3: Compute Weighted Means by Group

Often we are only interested to know the weighted mean for a subgroup of our data. Consider the following example data:

group <- c("A", "B", "A", "C", "C", "A", "B", "B") # Create group indicator
data <- data.frame(x1, w1, group)                  # Create data frame

 

example data weighted mean by group

Table 1: Example Data with Numeric Column, Weights & Group Indicator.

 

To compute the weighted mean by group we can use the functions of the dplyr package. Let’s install and load the package to R:

install.packages("dplyr")                          # Install dplyr package
library("dplyr")                                   # Load dplyr package

Now, we can calculate the weighted mean with the following R code:

data %>%                                           # Weighted mean by group
  group_by(group) %>% 
  summarise(weighted.mean(x1, w1))

 

dplyr package tibble with weighted means

Figure 1: dplyr Tibble Containing Weighted Means.

 

As you can see based on Figure 1, the previous R code returns a tibble with the weighted means by group to the RStudio console.

 

Alternative 1: weightedMean Function of matrixStats Package

The beauty of R is that there are always several ways to achieve a goal. Of cause, this is also true for the computation of the weighted mean. In the following two examples, I will therefore show some alternatives to the weighted.mean function.

Let’s start with the weightedMean function of the matrixStats package. First, we need to install and load the package…

install.packages("matrixStats")                    # Install matrixStats package
library("matrixStats")                             # Load matrixStats package

…and then we can apply the weightedMean R function as follows:

weightedMean(x1, w1)                               # Apply weightedMean function
# 4.965517

The same result as in Example 1 – looks good!

 

Alternative 2: wt.mean Function of SDMTools Package

Another alternative is the wt.mean function of the SDMTools package:

install.packages("SDMTools")                       # Install SDMTools package
library("SDMTools")                                # Load SDMTools package

After installing and loading the R package, we can apply the wt.mean command as follows:

wt.mean(x1, w1)                                    # Apply wt.mean function
# 4.965517

Again, the same result.

 

Further Resources & Summary

This article illustrated how to compute weighted means in the R programming language. In case you want to learn more the theoretical research concept of the weighted arithmetic mean, I can recommend the following video tutorial of the MySecretMathTutor YouTube channel:

 

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In addition, you may also have a look at some of the related R tutorials that I have published on this website:

I hope this tutorial contained the content you were looking for. However, don’t hesitate to let me know in case you have any comments or questions.

 



2 Comments. Leave new

  • Altamash Bashir
    April 7, 2020 4:55 pm

    Your description for calculating wtd mean was helpful but it was only with one variable. How to find weighted standard deviation or mean for many columns in the database

    Reply
    • Hi Altamash,

      I’m sure there are more efficient ways, but one solution might be to use a for-loop. Consider the following example:

      x1 <- c(9, 5, 2, 7, 3, 6, 4, 5)
      x2 <- c(7, 7, 9, 5, 2, 7, 3, 6)
      w1 <- c(2, 3, 1, 5, 7, 1, 3, 7)   
       
      data <- data.frame(x1, x2, w1)
       
      weighted_columns <- numeric()
      for(i in 1:(ncol(data) - 1)) {
        weighted_columns[i] <- weighted.mean(data[ , i], w1)
      }

      The weighted means of x1 and x2 are stored in the data object weighted_columns.

      I hope that helps!

      Joachim

      Reply

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