Question

Use the assumed-mean method to find the mean weekly wages from the data given below.$\begin{array}{cccccccc}\text{Weekly Wages (in Rs.)}& 800& 820& 860& 900& 920& 980& 1000\\ \text{No. of Workers}& 7& 14& 19& 25& 20& 10& 5\end{array}$

Answer 1

Let the assumed mean be A: $900$

Now, we will prepare the following table:

$\begin{array}{cccc}\text{Weekly Wages}\left(x_i\right)& \text{No. of workers}\left(f_i\right)& d_i=x_i-A=(x_i-900)& f_i{d}_i\\ 800& 7& -100& -700\\ 820& 14& -80& -1120\\ 860& 19& -40& -760\\ 900=A& 25& 0& 0\\ 920& 20& 20& 400\\ 980& 10& 80& 800\\ 1000& 5& 100& 500\\ & \sum f_i=100& & \sum f_i{d}_i=-880\end{array}$

Thus, we have:

Mean, $\overline{x}=A+\frac{\sum f_i{d}_i}{\sum f_i}$

$=900+\frac{(-880)}{100}=900-\frac{88}{10}=\frac{9000-88}{10}=\frac{8912}{10}=Rs891.2$