Question

Calculate range and coefficient of range for the following distribution:

Class	:	1-5	6-10	11-15	16-20	21-25	26-30
Frequency	:	2	8	15	35	20	10

Answer 1

The given series is an inclusive series. For the calculation of range the given series must first be converted into exclusive series as follows:

Inclusive class	Exclusive class	Frequency
1−5	0.5−5.5	2
6−10	5.5−10.5	8
11−15	10.5−15.5	15
16−20	15.5−20.5	35
21−25	20.5−25.5	20
26−30	25.5−30.5	10

Range = Largest item (L) − Smallest item (S)
= 30.5 − 0.5 = 30

$$\begin{gathered} \mathrm{Coefficient}\mathrm{of}\mathrm{Range}=\frac{L\mathit{-}S}{L+S}=\frac{30.5-0.5}{30.5+0.5} \\ =\frac{30}{31}=0.97 \end{gathered}$$