# Lower Quartiles (Mathematics Glossary)

# What Is the Lower Quartile?

The lower quartile is the middle number between the smallest number and the median.It is the middle number of the lower half of a set of numbers.

The lower quartile is denoted

**Q**.

_{1}# Understanding the Lower Quartile and the Quartiles

The lower quartile is the lowest of the three quartiles.The three quartiles divide a set of numbers, that are in numerical order, into four equal groups:

- The middle quartile is also known as the median. It is the middle number in the set. It divides the set in two halves.
- The lower quartile is the middle number of the lower half. It divides the lower half in two.
- The upper quartile is the middle number of the upper half. It divides the upper half in two.

# Finding the Lower Quartile

There are different methods for finding the lower quartile, which give different values.- The Moore and McCabe method
**excludes**the median from the lower half. The lower quartile is the middle number of the lower half:

- The Tukey method
**includes**the median in the lower half. The lower quartile is the middle number of the lower half:

**Note:**When the lower half has an even number of numbers, the middle number is halfway between the middle two numbers. It is the mean of the middle two numbers:

Q_{1}= (3 + 4) ÷ 2 = 3.5 - The Mendenhall and Sincich method uses a formula to find the position of the lower quartile. The formula is shown below:

In this formula,**n**is how many numbers there are in the set. In our example,**n**is 11.

Position of QThe lower quartile is the 3_{1}= (n + 1) ÷ 4 = (11 + 1) ÷ 4

Position of Q_{1}= 12 ÷ 4

Position of Q_{1}= 3^{rd}^{rd}number in the set:

##### Interactive Test

**show**

Here's a second test on the lower quartile.

Here's a third test on the lower quartile.

##### Note

# What Is a Quartile?

A quartile is one of three numbers that divide a set into four equal groups.A quartile can also describe each of the four groups.

# What's In a Name?

Quartile comes from the Latin word 'quartus', meaning 'a fourth'. It comes from the same root as 'quarter'.# The Other Quartiles

The lower quartile is just one of the three quartiles. The other quartiles are:- The middle quartile (also called the median). It is the middle number of the whole set of numbers.
- The upper quartile. It is the middle number between the median and the highest number.

Read more about the methods for finding the quartiles

##### Beware

# Put Your Numbers in Order

The quartiles of a set of numbers divide the numbers into four equal groups**when the numbers are in order**.

Imagine you were asked to find the lower quartile of the numbers below. Don't be tempted to jump right in.

3

Put the numbers in order and then find the lower quartile:**1**2 5 4
1

**2**3 4 5