Question

Find out range and coefficient of range from the following data

$\begin{array}{cccccc}\text{Marks}& 20-29& 30-39& 40-49& 50-59& 60-69\\ \text{Number of Students}& 8& 12& 20& 7& 3\end{array}$

Answer 1

As per the question inclusive series of marks and number of students are given. For calculating range and coefficient of range, firstly we will convert inclusive series into exclusive series and after that we will use the largest and smallest value of the exclusive series of marks.

$\begin{array}{cccccc}\text{Marks}& 20-29& 30-39& 40-49& 50-59& 60-69\\ \text{Exclusive Group}& 19.5-29.5& 29.5-39.5& 39.5-49.5& 49.5-59.5& 59.5-69.5\\ \text{Freq. (f)}& 8& 12& 20& 7& 3\end{array}$

Range = L - S

Here, L = Largest value, S = Smallest value, L = 69.5, S = 19.5

Range = 69.5 - 19.5 = 50

Coefficient of Range $=\frac{L-S}{L+S}=\frac{69.5-19.5}{69.5+19.5}$

$=\frac{50}{89}=0.56$