Question

Find out range and coefficient of range of the following series. $\begin{array}{cccccc}\text{Size}& 5-10& 10-15& 15-20& 20-25& 25-30\\ \text{Frequency}& 4& 9& 15& 30& 40\end{array}$

Answer 1

$\begin{array}{ccc}\text{Size}& \text{Mid-value}& \text{Frequency}\\ 5-10& 7.5& 4\\ 10-15& 12.5& 9\\ 15-20& 17.5& 15\\ 20-25& 22.5& 30\\ 25-30& 27.5& 40\end{array}$

Range $=H-L$, where $H=$ highest value of mid-value, $L=$ lowest value of mid-value

$=27.5-7.5=20$

Coefficient of range $=\frac{H-L}{H+L}$

$=\frac{27.5-7.5}{27.5+7.5}$

$=\frac{20}{35}=0.57$