# Upper Quartiles (Mathematics Glossary)

# What Is the Upper Quartile?

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

The upper quartile is denoted

**Q**.

_{3}# Understanding the Upper Quartile and the Quartiles

The upper quartile is the highest 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 Upper Quartile

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

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

**Note:**When the upper 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_{3}= (8 + 9) ÷ 2 = 8.5 - The Mendenhall and Sincich method uses a formula to find the position of the upper 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 upper quartile is the 9_{3}= 3(n + 1) ÷ 4 = 3 × (11 + 1) ÷ 4

Position of Q_{3}= 36 ÷ 4

Position of Q_{3}= 9^{th}^{th}number in the set:

##### Interactive Test

**show**

Here's a second test on the upper quartile.

Here's a third test on the upper 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 upper quartile is just one of the three quartiles. The other quartiles are:- The lower quartile. It is the middle number between the smallest number and the median.
- The middle quartile (also called the median). It is the middle number of the whole set of numbers.

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 upper quartile of the numbers below. Don't be tempted to jump right in.

3 1 2

Put the numbers in order and then find the upper quartile:**5**4
1 2 3

**4**5