Quartiles

Quartiles

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

How to Find

First find the median of the data, which is Q2. Then Q1 is the median of the left data. And Q3 is the median of the right data. These Q1, Q2, and Q3 are the quartiles of the data.

The quartiles are the values
that divide the data into 4 parts.

So there are three quartiles:
Q1, Q2, and Q3.

To find the quartiles,
first find the median of the data.

Median

Then Q1 is the median of the left half.
(It's also called the [lower quartile].)

Q2 is the median of the whole data.

Q3 is the median of the right half.
(It's also called the [upper quartile].)

Example 1: n is an Odd Number

For the given data below, find the quartiles.

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 Q2 = 6.

Median

Find the median of the left half.
Q2 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 Q1 = 4.

If your teacher says to include Q2 into the left half,
do what your teacher says.

Find the median of the right half.
Q2 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 Q3 = 7.

So Q1 = 4, Q2 = 6, Q3 = 7
are the quartiles of the given data.

Example 2: n is an Even Number

For the given data below, find the quartiles.

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 Q2 = 6.5.

Median

Q2 = 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 Q1 = 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 Q3 = 7.

So Q1 = 4, Q2 = 6.5, Q3 = 7
are the quartiles of the given data.