# Lower Quartile

## 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: a lower half and an upper half.

• The lower quartile is the middle number of the bottom half. It divides the bottom 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: 