The interquartile range represents the difference between the first quartile (the 25th percentile) and the third quartile (the 75th percentile) of a dataset.

In simple terms, it measures the spread of the middle 50% of values.

IQR = Q3 – Q1

We can use the built-in IQR() function to calculate the interquartile range of a set of values in R:

IQR(x)

The following examples show how to use this function in practice.

Example 1: Interquartile Range of a Vector

The following code shows how to calculate the interquartile range of values in a vector:

#define vector
x <- c(4, 6, 6, 7, 8, 12, 15, 17, 20, 21, 21, 23, 24, 27, 28)

#calculate interquartile range of values in vector
IQR(x)

[1] 14.5

Example 2: Interquartile Range of a Vector with Missing Values

If your vector has missing values, be sure to specify na.rm=TRUE to ignore missing values when calculating the interquartile range:

#define vector with some missing values
x <- c(4, 6, NA, 7, NA, NA, 15, 17, 20, 21, 21, 23, 24, 27, 28)

#calculate interquartile range of values in vector
IQR(x, na.rm=TRUE)

[1] 10.25

Example 3: Interquartile Range of Column in Data Frame

The following code shows how to calculate the interquartile range of a specific column in a data frame:

#define data frame
df <- data.frame(var1=c(1, 3, 3, 4, 5),
                 var2=c(7, 7, 8, 3, 2),
                 var3=c(3, 3, 6, 6, 8),
                 var4=c(1, 1, 2, 8, 9))

#calculate interquartile range of 'var1' column
IQR(df$var1)

[1] 1

Example 4: Interquartile Range of Several Columns in Data Frame

The following code shows how to calculate the interquartile range of several columns in a data frame:

#define data frame
df <- data.frame(var1=c(1, 3, 3, 4, 5),
                 var2=c(7, 7, 8, 3, 2),
                 var3=c(3, 3, 6, 6, 8),
                 var4=c(1, 1, 2, 8, 9))

#calculate interquartile range of 'var1', 'var2', and 'var4' columns
sapply(df[ , c('var1', 'var2', 'var4')], IQR)

var1 var2 var4 
   1    4    7