# Upper Quartile

## 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 Q3.

## 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:

Q3 = (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 Q3 = 3(n + 1) ÷ 4 = 3 × (11 + 1) ÷ 4

Position of Q3 = 36 ÷ 4

Position of Q3 = 9th

The upper quartile is the 9th number in the set: 