weighted.mean

Usage

Used to calculate the weighted mean of a variable.

Usage 1:

weighted.mean(dataframe$variable, dataframe$weights, na.rm=TRUE)
  • This calculates the weighted mean of variable in dataframe using weights as weights.
  • We always include na.rm=TRUE as the third input to tell R to remove any NA values from the calculation.

Usage 2:

some_dataframe_name <- dataframe %>%
  group_by(groupvar1, groupvar2, ...) %>%
  summarize(
    avg_variable = weighted.mean(variable, weights, na.rm=TRUE)
  )
  • This calculates the weighted mean of variable in dataframe within each possible combination of values for groupvar1, groupvar2, …
  • See the vignette on summary statistics for more details

Example 1 

rm(list=ls())

df <- read.csv("IPUMS_ACS2019_CA_1.csv")

weighted.mean(df$AGE, df$PERWT, na.rm=TRUE)

This calculates the weighted mean of AGE in df using PERWT as weights.

Example 2 

rm(list=ls())
library(dplyr)

df <- read.csv("IPUMS_ACS2019_CA_1.csv")

df$EMPLOYED <- df$EMPSTAT==1

emprate_by_race <- df %>%
  group_by(RACHSING) %>% 
  summarize(
    EMPLOYMENT_RATE = weighted.mean(EMPLOYED, PERWT, na.rm=TRUE)
  )

This calculates the weighted mean of EMPLOYED (e.g. the employment rate) within each value of RACHSING (e.g. by race), using PERWT as the weights.

Mathematical Background

Suppose you have \(N\) samples of a variable:

\[(x_1, x_2, x_3, \ldots, x_N)\]

Along with \(N\) weights:

\[(w_1, w_2, w_3, \ldots, w_N)\]

The weighted mean of \(x\) using \(w\) as weights is:

\[\frac{ \sum_{i=1}^{N} x_i w_i }{ \sum_{i=1}^{N} w_i }\]