Question

Find out quartile deviation and the coefficient of range, given the following data-set:

Class Interval	1−5	6−10	11−15	16−20	21−25	26−30	31−35
Frequency	2	8	15	35	20	10	14

Answer 1

In order to calculate range and its coefficient, we must first convert the given inclusive class intervals in exclusive class intervals.

Class Interval	Exclusive Class Interval	$\mathbf{Mid}\mathbf{}\mathbf{Value}=\frac{{\mathit{L}}_{\mathbf{1}}\mathbf{+}{\mathit{L}}_{\mathbf{2}}}{\mathbf{2}}$	Frequency
1 − 5 6 − 10 11 − 15 16 − 20 21 − 25 26 − 30 31 − 35	0.5 − 5.5 5.5 − 10.5 10.5 − 15.5 15.5 − 20.5 20.5 − 25.5. 25.5. − 30.5 30.5 − 35.5	3 8 13 18 23 28 33	2 8 15 35 20 10 14

$$\begin{gathered} \mathrm{Range}=Upper\mathrm{Limit}\mathrm{of}\mathrm{the}\mathrm{Highest}\mathrm{Class}\mathrm{Interval}-\mathrm{Lower}\mathrm{Limit}\mathrm{of}\mathrm{the}\mathrm{Lowest}\mathrm{Class}\mathrm{Interval} \\ \mathrm{or},\mathrm{Range}=35.5-0.5=35 \end{gathered}$$

$\mathrm{Coefficient}\mathrm{of}\mathrm{Range}=\frac{H-L}{H+L}=\frac{35.5-0.5}{35.5+0.5}=\frac{35}{36}=0.972$