Measures of Dispersion (Part 2)

Posted on April 21, 2020 by user

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

$\frac{14 + 16}{2} - \frac{4 + 6}{2}$

= 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

$\frac{1}{4} {(24)}^{th}$ observation

= the 6^thobservation

= 2

Upper quartile, Q₃= the

$\frac{3}{4} {(24)}^{th}$ observation

= the 18^thobservation

= 4

Interquartile Range

= upper quartile – lower quartile

= Q₃– Q₁

= 4 – 2

= 2