Calculate harmonic mean in R (with examples)

Renesh Bedre    1 minute read

Harmonic mean

Harmonic mean (HM) is a reciprocal of the arithmetic mean of the reciprocal of given numbers.

There should be no zero number in the dataset, otherwise harmonic mean will be zero. The harmonic mean is commonly used for calculating the mean of rates or ratios (e.g. speed of the car) as it gives more accurate answers than arithmetic means.

harmonic mean formula

Steps in harmonic mean calculation

For example, if we have three numbers of observations (e.g., 2, 5, 8),

steps in harmonic mean calculation

Calculate harmonic mean in R

Example: The speed of three motorbikes is 10 mph, 20 mph, and 60 mph. Calculate the harmonic mean of the motorbike’s speed.

You can calculate the harmonic mean of the speed of motorbike’s using the harmonic.mean() function available in the psych package. harmonic.mean() function takes the following arguments,

x: a vector, matrix, or data.frame
na.rm: if TRUE, drop NA values
zero: if TRUE, return 0 if there are any 0 values. Otherwise, return harmonic mean of non-zero numbers 

library("psych") 

x <- c(10, 20, 60)
harmonic.mean(x)
# output
18

The harmonic mean of the speed of three motorbikes is 18 mph.

If you have a data frame, you can also calculate the harmonic mean from data frame columns,

# create a sample data frame
df <- data.frame(bike=c("A", "B", "C"),
                speed=c(10, 20, 60))

# view data frame
df
  bike speed
1    A    10
2    B    20
3    C    60

# calculate harmonic mean
library("psych")
harmonic.mean(df$speed)
# output
18

Calculate harmonic mean from scratch in R

First, calculate the arithmetic mean of the reciprocal of given non-zero numbers,

m <- mean(c(1/10, 1/20, 1/60))

Now, get the reciprocal of the arithmetic mean,

hm <- 1/m
hm
# output
18

The harmonic mean of the speed of three motorbikes is 18 mph.

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