Quartile

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

Definition

Definition

The quartiles (Q1, Q2, Q3) are the numbers
that divide the data into 4 parts.

Example 1

Example

Solution

First find Q2.

Q2 is the median of the data.

The median of the data is
this 6.

So Q2 = 6.

Next, see the values
on the left side of Q2.

Q1 is the median of these values.

The median is
4.

So Q1 = 4.

Next, see the values
on the right side of Q2.

Q3 is the median of these values.

The median is
this 7.

So Q3 = 7.

Write Q1, Q2, and Q3.

So
Q1 = 4
Q2 = 6
Q3 = 7
is the answer.

Example 2

Example

Solution

First find Q2.

Q2 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 Q2 = 6.5.

Next, see the values
on the left side of Q2.

The value 6
is in the left side of Q2 = 6.5.
So include the value 6.

Q1 is the median of these values.

The median is
4.

So Q1 = 4.

Next, see the values
on the left side of Q3.

This value 7
is in the right side of Q2 = 6.5.
So include this value 7.

Q3 is the median of these values.

The median is
this 7.

So Q3 = 7.

Write Q1, Q2, and Q3.

So
Q1 = 4
Q2 = 6.5
Q3 = 7
is the answer.