weighted.mean

• Usage
• Example 1
• Example 2
• Mathematical Background

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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

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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.

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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.

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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:

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