## Quartiles

Table of Contents

## Definition of Quartiles

What are Quartiles?

In statistics, Quartiles are values that divide your data into quarters. They aren’t shaped like pizza slices. Quartiles divide your data into 4 segments according to where the numbers fall on the number line. The 4 quarters that divide a data set into quartiles are:

- Lowest 25% of numbers.
- Next lowest 25% of numbers up to the median.
- Second highest 25% of numbers above the median.
- Highest 25% of numbers.

You have to put the numbers in order to figure out where the quartiles are, because quartiles divide numbers up according to where their position is on the number line.

## Why do we need quartiles in statistics?

They’re used to perform further calculations, for example is the interquartile range, which is a measure of how the data is spread out around the mean.

## Upper Quartile

The upper quartile (also known as Q3) is the number dividing the 3^{rd} and 4^{th} quartile. It can also be thought of as the median of the upper half of the numbers. The upper quartile is also called the 75^{th} percentile because it splits the lowest 75% of data from the highest 25%.

## How to Find Quartiles

Quartiles are the values that divide a list of numbers into quarters:

- Put the list of numbers in order
- Then cut the list into four equal parts
- The Quartiles are at the “cuts”

6, 8, 4, 3, 6, 2, 9

Put them in order: 2, 3, 4, 6, 6, 8, 9

Cut the list into quarters:

Q1 | Q2(Median) | Q3 | ||||

2 | 3 | 4 | 6 | 6 | 8 | 9 |

And the result is:

- Quartile 1 (Q1) / Lower Quartile = 3
- Quartile 2 (Q2) / middle Quartile, which is also the Median, = 6
- Quartile 3 (Q3) / upper Quartile = 8

## Quartile Between 2 Numbers

Sometimes the “cut” is between 2 numbers.

The Quartile is the average of those 2 numbers.

1, 2, 2, 3, 4, 5, 5, 6, 7, 7

The numbers are already in order

Cut the list into quarters:

Q1 | Q2(Median) | Q3 | ||||||||

1 | 2 | 2 | 3 | 4 | 5 | 5 | 6 | 7 | 7 |

In this case Quartile 2 is half way between 4 and 5:

Q2 = (4+5)/2 = 4.5

And the result is:

- Quartile 1 (Q1) = 2
- Quartile 2 (Q2) = 4.5
- Quartile 3 (Q3) = 6

## Interquartile Range

The “Interquartile Range” is from Q1 to Q3.

To calculate it just subtract Quartile 1 from Quartile 3

Interquartile Range = Q3 – Q1

Q1 | Q2(Median) | Q3 | ||||

2 | 3 | 4 | 6 | 6 | 8 | 9 |

The Interquartile Range is = Q3 − Q1 = 8 − 3 = 5

## Quartile Function in Excel

You can find a quartile in Microsoft Excel using the Excel quartile function.

Type your data into a single column. (For example, type your data into cells A1 to A10)

Click an empty cell somewhere on the sheet. (For example, click cell B1)

Type “=QUARTILE(A1:A10,1)” and then press “Enter”. (This finds the first quartile. To find the third quartile, type “=QUARTILE(A1:A10,3)”)

Note: If your data is in a different cell range other than A1:A10, make sure you change the function to reflect that.