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 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) ÷ 4
Position of Q_{3} = 36 ÷ 4
Position of Q_{3} = 9^{th}
The upper quartile is the 9^{th} number in the set: