Calculate the Interquartile Range in R Programming – IQR() Function

The first quartile (Q1) and the third quartile (Q3) of a dataset are represented by the interquartile range (IQR), a statistical measure of statistical dispersion. Particularly for the middle 50% of the sample, it offers insightful information regarding the distribution and variability of the data.

Here are the steps how to compute the IQR:

1. Sort the dataset by highest to lowest value.
2. Find the first quartile’s (Q1) location. The dataset is divided into the lowest 25% of values in the first quartile.
3. Find the third quartile’s (Q3) location. The dataset is divided into the lowest 75% of values at the third quartile.

IQR() function in R Language is used to calculate the interquartile range of a data set.

Mathematically, IQR = Q3 – Q1 where, Q3 specifies the median of n largest values Q1 specifies the median of n smallest values

But, R provides an in-built IQR() function to perform the upgiven calculations

Syntax: IQR(x) Parameters: x: Data set

Calculate IQR for the vectors:

R

# R program to calculate IQR value

# Defining vector
x <- c(5, 5, 8, 12, 15, 16)

# Print Interquartile range
print(IQR(x))

Output:

[1] 8.5

Calculate IQR for the matrix:

R

# R program to calculate IQR value

# Defining a matrix
x <- matrix(c(1:9), 3, 3)

# Print Interquartile range
print(IQR(x))

Output:

[1] 4

Calculate IQR for the missing values:

With the help of na.rm=TRUE we can ignore missing values and calculate IQR.

R

# R program to calculate IQR value

# Defining vector
x <- c(5, 5,NA, 8,NA, 12,NA, 15, 16,18)

# Print Interquartile range
print(IQR((x),na.rm=TRUE))

Output:

[1] 9

Calculate IQR for the single columns of the dataframe:

We can load the iris dataset to calculate the IQR for single columns.

R

# load the dataset.
data(iris)

# calculate IQR for single column.
IQR(iris$Petal.Length)

Output:

[1] 3.5

Calculate IQR for the multiple columns of the dataframe:

With the help of apply function, we can calculate the IQR for multiple columns.

R

# load library
library(dplyr)

# remove Species column from dataset
data=select(iris,-('Species'))

# calculate the IQR for all columns
sapply(data,IQR)

Output:

Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
         1.3          0.5          3.5          1.5 

We can calculate the IQR for multiple columns in a dataset with the help of sapply function. we remove the species column from the data because the IQR function only works on numerical columns.