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Quartiles (Mathematics Glossary)

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 Merriam-Webster 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 Cut-Off Points

The quartiles refer to the three cut-off points that separate the four groups: the lower quartile (Q1), the middle quartile (Q2) and the upper quartile (Q3):

  • 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 Q1, Q2 and Q3:

  • 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.

Read more about the methods for finding the quartiles

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, Q3 is the upper quartile and Q1 is the lower quartile.

Read more about the interquartile range
Interactive Test
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Here's a second test on quartiles.
Here's a third test on quartiles.
Note

What's In a Name?

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

A Quartile Is a Quantile

A quartile is a type of quantile.

A quantile is a cut-of point which divides a set of numbers into equal groups.
  • A quartile divides a set of numbers into four equal groups.

  • A decile divides a set of numbers into ten equal groups.

  • A percentile divides a set of numbers into a hundred equal groups.
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 quartiles of the numbers below. Don't be tempted to jump right in.
3 2 4 5 1
Put the numbers in order and then find the quartile:
1 2 3 4 5