# Stats Review: How to Calculate Quartiles

This article explains how to calculate quartiles.

**Quartiles**

They represent the position of a given value within a set of data divided in four equal parts. The quartiles represent the first, second or third quarter.

__First quarter (Q1)__

Q1 = X to the position [1 (n + 1)] / 4

__Second quarter (Q2)__

Q2 = X to the position [2 (n + 1)] / 4

__Third quarter (Q3)__

Q3 = X to the position [3 (n + 1)] / 4

**If (n+1)/4 is equal to a whole number**

__Example #1:__

Data: 20 13 30 45 67 26 48

- Count the number of values present in the set of data

n = 7

- Rearrange the numbers in increasing order

13 20 26 30 45 48 67

- Using the quartile formulas, find the position for each quartile

Q1 = X to the position [1 (n + 1)] / 4 = [1 (7 + 1)] / 4 = 2nd position

Q2 = X to the position [2 (n + 1)] / 4 = [2 (7 + 1)] / 4 = 4th position

Q3 = X to the position [3 (n + 1)] / 4 = [3 (7 + 1)] / 4 = 6th position

- Find the value associated with each position

The value for the first quartile is 20, the value for the second quartile is 30 and the value for the third quartile is 48.

**If (n+1)/4 is not equal to a whole number**

__Example #2:__

Data: 15 27 52 24 37 17 22 29

- Count the number of values present in the set of data

n = 8

- Rearrange the numbers in increasing order

15 17 22 24 27 29 37 52

- Using the quartile formulas, find the position for each quartile

Q1 = X to the position [1 (n + 1)] / 4 = [1 (8 + 1)] / 4 = 2.25th position

Q2 = X to the position [2 (n + 1)] / 4 = [2 (8 + 1)] / 4 = 4.5th position

Q3 = X to the position [3 (n + 1)] / 4 = [3 (8 + 1)] / 4 = 6.75th position

- The values find themselves between values in the data, so we must interpolate the value

**The position of the value for Q1 is at the 2.25th position. This means that the value is between the numbers 17 and 22 from our data. The detailed calculation is stated below.

Q1 = 17 + (0.25*(22-17)) = 18.25 ≈ 18

** Repeat this process for Q2 and Q3

Q2 = 24 + (0.5*(27-24)) = 25.5 ≈ 26

Q3 = 29 + (0.75*(37-29)) = 35

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