7.2b Interquartile Range 1

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.
1        3        5        6        7        8        11
          ↑                  ↑                  ↑
      lower          median          upper
quartile                             quartile

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

(b) Rearrange the data according to ascending order.
2        4    ⁞    6        9    ⁞    12        14    ⁞     16        18
                ↑                   ↑                       ↑
             lower          median               upper
        quartile                                 quartile

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.

Marks
1
2
3
4
5
Number of students
4
7
5
2
6

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

Marks
Frequency
Cumulative Frequency
1
4
4
2
7
11 (Q1 is located here)
3
5
16
4
2
18 (Q3 is located here)
5
6
24

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

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