**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: a lower half and an upper half.
- 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 Q

_{3}= 3(n + 1) ÷ 4 = 3 × (11 + 1) ÷ 4Position of Q

_{3}= 36 ÷ 4Position of Q

_{3}= 9^{th}^{th}number in the set:

## What's In a Name?

Quartile comes from the Latin word "quartus", meaning 'a fourth'. It comes from the same root as 'quarter'.## 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 5 4

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

**4**5## You might also like...

statisticsunderstanding the lower quartilefinding the quartilesunderstanding the interquartile range

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.