7.2b Interquartile Range 2

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

(C) Interquartile Range of Grouped Data (with Class Interval)

The interquartile range of grouped data can be determined by Method 1 (using a cumulative frequency table) or Method 2 (using an ogive).


Example:
The table below shows the marks obtained by a group of Form 4 students in school mathematics test.
Marks
Frequency
20 – 29
4
30 – 39
8
40 – 49
20
50 – 59
16
60 – 69
9
70 – 79
3
Estimate the interquartile range.

Solution:
Method 1: From Cumulative Frequency Table
Step 1:
Lower quartile, Q1 = the   1 4 ( 60 ) th observation
                               = the 15thobservation

Upper quartile, Q3 = the   3 4 ( 60 ) th observation
                               = the 45thobservation


Marks
Frequency
Cumulative
frequency
20 – 29
4
4
30 – 39
8
12
40 – 49
20
32  (Q1 is located here)
50 – 59
16
48 (Q3 is located here)
60 – 69
9
57
70 – 79
3
60

Step 2:
Lower quartile,  Q 1 = L 1 + ( 1 4 N F 1 f Q 1 ) C                               = 39.5 + ( 15 12 20 ) 10                               = 39.5 + 1.5                               = 41
Step 3:
Upper quartile,  Q 3 = L 3 + ( 3 4 N F 3 f Q 3 ) C                                 = 49.5 + ( 45 32 16 ) 10                                 = 49.5 + 8.125                                 = 57.625
Step 4:
Interquartile Range
= upper quartile – lower quartile
= Q3Q1
= 57.625 – 41
= 16.625

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