# Interquartile Range (IQR) Calculator

An interquartile range (IQR) calculator is a useful tool for analyzing and interpreting statistical data. It helps users calculate the IQR, which is a measure of the spread or dispersion of a dataset. By inputting the values of a dataset, the calculator calculates the 25th percentile (Q1), 75th percentile (Q3), and the IQR as the difference between Q3 and Q1. This information allows users to understand the central tendency and variability of the dataset, identify outliers, and make comparisons between different datasets.

**Interquartile Range (IQR):**

_{1}):

_{2}):

_{3}):

## 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

## Interquartile Range (IQR) Calculator example

Certainly! Here's an example of calculating the interquartile range (IQR) using a dataset and a table:

Let's say we have the following dataset:

14, 19, 22, 25, 28, 30, 35, 38, 40, 45

To calculate the IQR, you'll need to follow these steps:

- Sort the dataset in ascending order:

14, 19, 22, 25, 28, 30, 35, 38, 40, 45

- Find the median (Q2), which is the middle value of the dataset:

Median = (28 + 30) / 2 = 29

- Split the dataset into two halves: the lower half and the upper half.

Lower Half: 14, 19, 22, 25

Upper Half: 35, 38, 40, 45

- Find the first quartile (Q1), which is the median of the lower half of the dataset:

Q1 = (19 + 22) / 2 = 20.5

- Find the third quartile (Q3), which is the median of the upper half of the dataset:

Q3 = (38 + 40) / 2 = 39

- Calculate the interquartile range (IQR) by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 39 - 20.5 = 18.5

So, in this example, the interquartile range (IQR) of the dataset is 18.5.

I hope this helps! Let me know if you have any further questions.