# Interquartile Range Calculator

## What is Interquartile Range Calculator?

'Cuemath's Interquartile Range Calculator' is an online tool that helps to calculate the interquartile range. Cuemath's online Interquartile Range calculator helps you to calculate the interquartile range within a few seconds.

## How to Use the Interquartile Range Calculator?

• Step 1: Enter the data set separated by a comma in the given input box.
• Step 2: Click on the "Calculate" button to find the interquartile range.
• Step 3: Click on the "Reset" button to find the interquartile range for different data.

## How to Find the Interquartile Range?

Quartile means a quantile that divides a ranked data into four equal parts. The Quartile which divides a given data set into four equal parts is known as the First quartile- Q1, second quartile- Q2, and Third quartile- Q3 respectively. The first quartile is also known as the lower quartile.

• Q1 is the mid-value of the first half.
• Q2 is the Median
• Q3 is the mid-value of the second half or last half.

Intermediate Quartile is defined as the difference between the third quartile(Q3) and first quartile(Q1)

Intermediate quartile = Q3 - Q1

The first quartile (or lower quartile) is the median or mid-value of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

The third quartile is the median or mid-value of the second half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

Note: 1) If the given data set has even numbers, Find the median from the bottom half and upper half

2) If the given data set has odd numbers, Find the median or average from the bottom half and upper half

### Solved Example 1:

Find the intermediate quartile from the given data set { 8, 6, 9, 2, 4, 5 }

### Solution:

Arrange this data set in increasing order i.e., {2, 4, 5, 6, 8, 9}

So, the bottom half is { 2, 4, 5 } and the upper half is {6, 8, 9}

The median of the bottom half(Q1) for { 2, 4, 5 } is 4.

The median of the upper half(Q3) for {6, 8, 9} is 8

Intermediate quartile = Q3 - Q1

= 8 - 4

= 4

Therefore, the intermediate quartile of the data set is 4.

### Solved Example 2:

Find the intermediate quartile from the given data set { 8, 6, 9, 2, 5 }

### Solution:

Arrange this data set in increasing order i.e., {2, 5, 6, 8, 9}

So, the bottom half is {2,5} and the upper half is {8, 9}

The median of the bottom half(Q1) for {2, 5} is 3.5

The median of the upper half(Q3) for {8, 9} is 8.5

Intermediate quartile = Q3 - Q1

= 8.5 - 3.5

= 5

Therefore, the intermediate quartile of the data set is 5

Similarly, you can try the calculator to find the intermediate quartile for the given data sets

1) {7, 12, 5, 8, 3}     2) {6, 2, 14, 7, 5, 6}