7.2b Interquartile Range 2 - SPM Additional Mathematics

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.

Estimate the interquartile range.

Solution:

Method 1: From Cumulative Frequency Table

Step 1:

Lower quartile, Q₁= the

\frac{1}{4} {(60)}^{th}

observation

= the 15^thobservation

Upper quartile, Q₃= the

\frac{3}{4} {(60)}^{th}

observation
= the 45^thobservation

Step 2:

\begin{array}{l} Lower quartile, Q_{1} = L_{1} + (\frac{\frac{1}{4} N - F_{1}}{f_{Q_{1}}}) C \\ = 39.5 + (\frac{15 - 12}{20}) 10 \\ = 39.5 + 1.5 \\ = 41 \end{array}

Step 3:

\begin{array}{l} Upper quartile, Q_{3} = L_{3} + (\frac{\frac{3}{4} N - F_{3}}{f_{Q_{3}}}) C \\ = 49.5 + (\frac{45 - 32}{16}) 10 \\ = 49.5 + 8.125 \\ = 57.625 \end{array}

Step 4:

Interquartile Range

= upper quartile – lower quartile

= Q₃– Q₁

= 57.625 – 41

= 16.625