Question

Question 7
The weights (in kg) of 50 wrestlers are recorded in the following table.
$\begin{array}{cccccc}\text{Weight(in~kg)}& 100-110& 110-120& 120-130& 130-140& 140-150\\ \text{Number of wrestlers}& 4& 14& 21& 8& 3\end{array}$
Find the mean weight of the wrestlers.

Answer 1

We first find the class mark $x_i$, of each class and then proceed as follows
$\begin{array}{ccccc}\text{Weight~(in~kg)}& \text{Number~of~wrestlers}\left(f_i\right)& \text{Class~marks}\left(x_i\right)& \text{Deviations}{d}_i=x_i-a& f_i{d}_i\\ 100-110& 4& 105& -20& -80\\ 110-120& 14& 115& -10& -140\\ 120-130& 21& a=125& 0& 0\\ 130-140& 8& 135& 10& 80\\ 140-150& 3& 145& 20& 60\\ & N=\sum f_i=50& & & \sum f_i{d}_i=-80\end{array}$
$\therefore$ Assumed mean (a) = 125,
Class width (h) = 10 and total observation (N) = 50
By assumed mean method,
Mean $\left(\overline{x}\right)=a+\frac{\sum f_i{d}_i}{\sum f_i}$
$=125+\frac{(-80)}{50}$
$=125-1.6=123.4kg$