# Quartile

How to find the quartiles (Q1, Q2, Q3) of the given data: definition, 2 examples, and their solutions.

## Definition

The quartiles (Q_{1}, Q_{2}, Q_{3}) are the numbers

that divide the data into 4 parts.

## Example

First find Q_{2}.

Q_{2} is the median of the data.

The median of the data is

this 6.

So Q_{2} = 6.

Next, see the values

on the left side of Q_{2}.

Q_{1} is the median of these values.

The median is

4.

So Q_{1} = 4.

Next, see the values

on the right side of Q_{2}.

Q_{3} is the median of these values.

The median is

this 7.

So Q_{3} = 7.

Write Q_{1}, Q_{2}, and Q_{3}.

So

Q_{1} = 4

Q_{2} = 6

Q_{3} = 7

is the answer.

## Example

First find Q_{2}.

Q_{2} is the median of the data.

The median of the data is

the mean of 6 and this 7.

The mean of 6 and 7 is

[6 + 7]/2 = 6.5.

So Q_{2} = 6.5.

Next, see the values

on the left side of Q_{2}.

The value 6

is in the left side of Q_{2} = 6.5.

So include the value 6.

Q_{1} is the median of these values.

The median is

4.

So Q_{1} = 4.

Next, see the values

on the left side of Q_{3}.

This value 7

is in the right side of Q_{2} = 6.5.

So include this value 7.

Q_{3} is the median of these values.

The median is

this 7.

So Q_{3} = 7.

Write Q_{1}, Q_{2}, and Q_{3}.

So

Q_{1} = 4

Q_{2} = 6.5

Q_{3} = 7

is the answer.