Measures of Dispersion (Part 2)

Measures of Dispersion (Part 2)
7.2b Interquartile Range 1

(A) Interquartile Range of Ungrouped Data



Example 1: 
Find the interquartile range of the following data.
(a) 7, 5, 1, 3, 6, 11, 8
(b) 12, 4, 6, 18, 9, 16, 2, 14

Solution:
(a) Rearrange the data according to ascending order.

Interquartile Range
= upper quartile – lower quartile
= 8 – 3
= 5 

(b) Rearrange the data according to ascending order.


Interquartile Range
= upper quartile – lower quartile
14 + 16 2 4 + 6 2
= 15 – 5
= 10


(B) Interquartile Range of Grouped Data (without Class Interval)

Example 2: 
The table below shows the marks obtained by a group of Form 4 students in school mid-term science test.


Determine the interquartile range of the distribution.

Solution:
Lower quartile, Q1 = the   1 4 ( 24 ) th observation
  = the 6thobservation
  = 2

Upper quartile, Q3 = the   3 4 ( 24 ) th observation
  = the 18thobservation
  = 4


Interquartile Range
= upper quartile – lower quartile
= Q3Q1
= 4 – 2
= 2