Interquartile Range (IQR)

21 May, 2021
The quartiles of a ranked set of data values are three points which divide the data into exactly four equal parts, each part comprising of quarter data.  
Q1 is defined as the middle number between the smallest number and the median of the data set.Q2 is the median of the data.Q3 is the middle value between the median and the highest value of the data set.
Q1 is defined as the middle number between the smallest number and the median of the data set.
Q2 is the median of the data.
Q3 is the middle value between the median and the highest value of the data set.
 
The interquartile range IQR tells us the range 
where the bulk of the values lie. The interquartile 
range is calculated by subtracting the first quartile
from the third quartile. 
IQR = Q3 - Q1
Uses 1. Unlike range, IQR tells where the majority of data lies and is thus preferred over range. 2. IQR can be used to identify outliers in a data set. 3. Gives the central tendency of the data. Examples:  
Input : 1, 19, 7, 6, 5, 9, 12, 27, 18, 2, 15
Output : 13
The data set after being sorted is 
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27
As mentioned above Q2 is the median of the data. 
Hence Q2 = 9
Q1 is the median of lower half, taking Q2 as pivot.
So Q1 = 5
Q3 is the median of upper half talking Q2 as pivot. 
So Q3 = 18
Therefore IQR for given data=Q3-Q1=18-5=13 

Input : 1, 3, 4, 5, 5, 6, 7, 11
Output : 3
 
C++
Java
Python3
C#
PHP
Javascript
// CPP program to find IQR of a data set#include <bits/stdc++.h>using namespace std; // Function to give index of the medianint median(int* a, int l, int r){    int n = r - l + 1;    n = (n + 1) / 2 - 1;    return n + l;} // Function to calculate IQRint IQR(int* a, int n){    sort(a, a + n);     // Index of median of entire data    int mid_index = median(a, 0, n);     // Median of first half    int Q1 = a[median(a, 0, mid_index)];     // Median of second half    int Q3 = a[mid_index + median(a, mid_index + 1, n)];     // IQR calculation    return (Q3 - Q1);} // Driver Functionint main(){    int a[] = { 1, 19, 7, 6, 5, 9, 12, 27, 18, 2, 15 };    int n = sizeof(a)/sizeof(a[0]);    cout << IQR(a, n);    return 0;}
// Java program to find// IQR of a data setimport java.io.*;import java .util.*; class GFG{     // Function to give// index of the medianstatic int median(int a[],                  int l, int r){    int n = r - l + 1;    n = (n + 1) / 2 - 1;    return n + l;} // Function to// calculate IQRstatic int IQR(int [] a, int n){    Arrays.sort(a);     // Index of median    // of entire data    int mid_index = median(a, 0, n);     // Median of first half    int Q1 = a[median(a, 0,                      mid_index)];     // Median of second half    int Q3 = a[mid_index + median(a,               mid_index + 1, n)];     // IQR calculation    return (Q3 - Q1);} // Driver Codepublic static void main (String[] args){    int []a = {1, 19, 7, 6, 5, 9,               12, 27, 18, 2, 15};    int n = a.length;    System.out.println(IQR(a, n));}} // This code is contributed// by anuj_67.
# Python3 program to find IQR of# a data set # Function to give index of the mediandef median(a, l, r):    n = r - l + 1    n = (n + 1) // 2 - 1    return n + l # Function to calculate IQRdef IQR(a, n):     a.sort()     # Index of median of entire data    mid_index = median(a, 0, n)     # Median of first half    Q1 = a[median(a, 0, mid_index)]     # Median of second half    Q3 = a[mid_index + median(a, mid_index + 1, n)]     # IQR calculation    return (Q3 - Q1) # Driver Functionif __name__=='__main__':    a = [1, 19, 7, 6, 5, 9, 12, 27, 18, 2, 15]    n = len(a)    print(IQR(a, n)) # This code is contributed by# Sanjit_Prasad
// C# program to find// IQR of a data setusing System; class GFG{     // Function to give// index of the medianstatic int median(int []a,                int l, int r){    int n = r - l + 1;    n = (n + 1) / 2 - 1;    return n + l;} // Function to// calculate IQRstatic int IQR(int [] a, int n){    Array.Sort(a);     // Index of median    // of entire data    int mid_index = median(a, 0, n);     // Median of first half    int Q1 = a[median(a, 0,                    mid_index)];     // Median of second half    int Q3 = a[mid_index + median(a,            mid_index + 1, n)];     // IQR calculation    return (Q3 - Q1);} // Driver Codepublic static void Main (){    int []a = {1, 19, 7, 6, 5, 9,            12, 27, 18, 2, 15};    int n = a.Length;    Console.WriteLine(IQR(a, n));}} // This code is contributed// by anuj_67.
<?php// PHP program to find IQR of a data set // Function to give index of the medianfunction median($a, $l, $r){    $n = $r - $l + 1;    $n = (int)(($n + 1) / 2) - 1;    return $n + $l;} // Function to calculate IQRfunction IQR($a, $n){    sort($a);     // Index of median of entire data    $mid_index = median($a, 0, $n);     // Median of first half    $Q1 = $a[median($a, 0, $mid_index)];     // Median of second half    $Q3 = $a[$mid_index + median($a, $mid_index + 1, $n)];     // IQR calculation    return ($Q3 - $Q1);} // Driver Function$a = array( 1, 19, 7, 6, 5, 9,            12, 27, 18, 2, 15 );$n = count($a);echo IQR($a, $n); // This code is contributed by mits?>
<script> // javascript program to find// IQR of a data set // Function to give// index of the medianfunction median(a, l , r){    var n = r - l + 1;    n = parseInt((n + 1) / 2) - 1;    return parseInt(n + l);} // Function to// calculate IQRfunction IQR(a , n){    a.sort((a,b)=>a-b);     // Index of median    // of entire data    var mid_index = median(a, 0, n);     // Median of first half    var Q1 = a[median(a, 0,                      mid_index)];     // Median of second half    var Q3 = a[mid_index + median(a,               mid_index + 1, n)];     // IQR calculation    return (Q3 - Q1);} // Driver Codevar a = [1, 19, 7, 6, 5, 9,         12, 27, 18, 2, 15];var n = a.length;document.write(IQR(a, n));  // This code contributed by Princi Singh</script>
Output:  
13
Reference https://en.wikipedia.org/wiki/Interquartile_rangeThis article is contributed by Vineet Joshi. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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