# 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 Q1.

# 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:
Q1 = (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 Q1 = (n + 1) ÷ 4 = (11 + 1) ÷ 4
Position of Q1 = 12 ÷ 4
Position of Q1 = 3rd
The lower quartile is the 3rd 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.

# 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.
There are different methods for finding the quartiles, which give different values.