# Interquartile Range (IQR) Calculator

You can use this interquartile range calculator to determine the interquartile range of a set of numbers, including the first quartile, third quartile, and median.

**Interquartile Range (IQR):**

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## How to use the Interquartile Range Calculator:

1) Enter each of the numbers in your set separated by a comma (e.g., 1,9,11,59,77), space (e.g., 1 9 11 59 77) or line break.

2) Click on the "Calculate" button to calculate the interquartile range.

## What is an Interquartile Range?

The interquartile range (IQR) is the range from the 25^{th} percentile to the 75^{th} percentile, or middle 50 percent, of a set of numbers. It is frequently calculated as a means of identifying what the range of an average performance should be. For example, how students will typically perform on an exam or the salary levels of a set of employees working in a given industry.

Many people argue that the interquartile range represents a more effective measurement than the median or mean because it provides insights into how the data is dispersed as opposed to giving a single number.

## An Example of Calculating IQR Using an IQR Formula

To identify the interquartile range of a set of data, simply subtract the first quartile from the third quartile as follows:

IQR = Q_{3} - Q_{1}

Where Q_{1} is the first, or lower quartile, and Q_{3} is the third, or upper quartile.

For example, let's say we need to determine the IQR of the following set of data 1, 4, 2, 6, 8, 10, 11, 5.

The set of numbers of interest is as follows: 1, 4, 2, 6, 8, 10, 11, 5.

First, place the numbers in ascending order: 1, 2, 4, 5, 6, 8, 10, 11.

Then, identify the 1st and 3rd quartiles as follows:

1st Quartile = (2 + 4) / 2 = 6 / 2 = 3

3rd Quartile = (8 + 10) / 2 = 18 / 2 = 9

Median = 5.5

The interquartile range (IQR) = 3rd Quartile - 1st Quartile

IQR = 9 - 3 = 6

You may also be interested in our Percentile Calculator