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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