Question

The following table shows the weights of $12$ workers in a factory:

$\begin{array}{cccccc}\text{Weight (in kg)}& 60& 63& 66& 69& 72\\ \text{No. of workers}& 4& 3& 2& 2& 1\end{array}$

Find the mean weight of the workers.

Answer 1

For calculating the mean, we prepare the following frequency table:

$\begin{array}{ccc}\text{Weight (in kg)}\left(x_i\right)& \text{No. of workers}\left(f_i\right)& f_i{x}_i\\ 60& 4& 240\\ 63& 3& 189\\ 66& 2& 132\\ 69& 2& 138\\ 72& 1& 72\\ & \sum f_i=12& \sum f_i{x}_i=771\end{array}$

Mean weight olf the worker, $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{771}{12}$

$=64.25kg$

Thus, the mean weight of the workers is $64.25kg$