# Quartiles

How to find the first, second, and third quartiles of the given data: how to find, examples, and their solutions.

## How to Find

The quartiles are the values

that divide the data into 4 parts.

So there are three quartiles:*Q*_{1}, *Q*_{2}, and *Q*_{3}.

To find the quartiles,

first find the median of the data.

Median

Then *Q*_{1} is the median of the left half.

(It's also called the [lower quartile].)*Q*_{2} is the median of the whole data.*Q*_{3} is the median of the right half.

(It's also called the [upper quartile].)

## Example 1: *n* is an Odd Number

First find the median of the data.

The number of the data is 15:

an odd number.

So the median is the middle value: 6.

So *Q*_{2} = 6.

Median

Find the median of the left half.*Q*_{2} is excluded from the left half.

The number of the left half data is 7:

an odd number.

So the median is the middle value: 4.

So *Q*_{1} = 4.

If your teacher says to include *Q*_{2} into the left half,

do what your teacher says.

Find the median of the right half.*Q*_{2} is excluded from the left half.

The number of the right half data is 7:

an odd number.

So the median is the middle value: 7.

So *Q*_{3} = 7.

So *Q*_{1} = 4, *Q*_{2} = 6, *Q*_{3} = 7

are the quartiles of the given data.

## Example 2: *n* is an Even Number

First find the median of the data.

The number of the data is 14:

an even number.

So the median is

the mean of the two middle numbers:

(6 + 7)/2 = 6.5.

So *Q*_{2} = 6.5.

Median

*Q*_{2} = 6.5 is

between the two middle numbers 6 and 7.

So include the middle value 6

into the left half:

1, 2, 4, 4, 5, 5, 6.

And include the other middle value 7

into the right half:

7, 7, 7, 7, 8, 8, 9.

Find the median of the left half.

The number of the left half data is 7:

an odd number.

So the median is the middle value: 4.

So *Q*_{1} = 4.

Find the median of the right half.

The number of the right half data is 7:

an odd number.

So the median is the middle value: 7.

So *Q*_{3} = 7.

So *Q*_{1} = 4, *Q*_{2} = 6.5, *Q*_{3} = 7

are the quartiles of the given data.