Question

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. Using the step - deviation method find the mean.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

• A. 58
• B. 55.77
• C. 65
• D. 62.5

Answer 1

The correct option is B 55.77

$\begin{array}{ccccc}\text{Class}& \text{Mid value}& \text{Frequency}& \mu =\frac{x-a}{h}& f_i{u}_i\\ \text{Interval}& \left(x_i\right)& \left(f_i\right)& & \\ 0-10& 5& 10& -5& -50\\ 10-20& 15& 12& -4& -48\\ 20-30& 25& 15& -3& -45\\ 30-40& 35& 8& -2& -16\\ 40-50& 45& 20& -1& -20\\ 50-60& 55=a& 24& 0& 0\\ 60-70& 65& 7& 1& 7\\ 70-80& 75& 11& 2& 22\\ 80-90& 85& 30& 3& 90\\ 90-100& 95& 18& 4& 72\\ \text{Total}& & \sum f_i=155& & \sum f_i{u}_i=12\end{array}$

Let, the assumed mean (a) = 55.
Class width (h) = 10

$\therefore Mean=a+\frac{\Sigma fu}{\Sigma f}\times h$

$=55+\frac{12}{155}\times 10$

$=55+0.77$

$=55.77$