Quartiles
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.
Dictionary Definition
The MerriamWebster dictionary defines a quartile as "any of the three values that divide the items of a frequency distribution into four classes with each containing one fourth of the total population; also: any one of the four classes."
Understanding a Quartile
We can divide a set of numbers, that are in numerical order, into four equal groups.
Quartiles As CutOff Points
The quartiles refer to the three cutoff points that separate the four groups: the lower quartile (Q_{1}), the middle quartile (Q_{2}) and the upper quartile (Q_{3}):

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 bottom half. It divides the bottom half in two.

The upper quartile is the middle number of the top half. It divides the top half in two.
Quartiles As Groups
The quartiles also refer to the four equal groups that are separated by Q_{1}, Q_{2} and Q_{3}:

A quarter of the numbers are below the lower quartile.

A quarter of the numbers are between the lower quartile and the median.

A quarter of the numbers are between the median and the upper quartile.

A quarter of the numbers are above the upper quartile.
Finding the Quartiles
There are different methods for finding the three quartile values (the lower quartile, the middle quartile and the upper quartile), which give different answers.
The Interquartile Range
The interquartile range is the difference between the upper quartile and the lower quartile. It is the range of the middle half of the data in a set.
The interquartile range is found using the formula:
In this formula, IQR is the interquartile range, Q_{3} is the upper quartile and Q_{1} is the lower quartile.