Question

Question 5
The daily income of a sample of 50 employee are tabulated as follows.
$\begin{array}{ccccc}\text{Income(in~Rs)}& 1-200& 201-400& 401-600& 601-800\\ \text{Number of employees}& 14& 15& 14& 7\end{array}$
Find the mean daily income of employees.

Answer 1

Since given data is not continuous, we subtract 0.5 from the lower limit and add 0.5 in the upper limit of each class.
Now we first, find the class mark $x_i$ of each class and then proceed as follows
$\begin{array}{ccccc}\text{Income (in~Rs)}& \text{Class~marks}\left(x_i\right)& \text{Number of employees}\left(f_i\right)& u_i=\frac{x_i-a}{h}=\frac{x_i-300.5}{200}& f_i{u}_i\\ 0.5-200.5& 100.5& 14& -1& -14\\ 200.5-400.5& a=300.5& 15& 0& 0\\ 400.5-600.5& 500.5& 14& 1& 14\\ 600.5-800.5& 700.5& 7& 2& 14\\ & & N=\sum f_i=50& & \sum f_i{u}_i=14\end{array}$
$\therefore$ Assumed mean, a = 300.5
Class width, h = 200
and total observations, N = 50
By step deviatin method,
$Mean=a+h\times \frac{1}{N}\times {\sum }_{i=1}^4{f}_i{u}_i$
$=300.5+200\times \frac{1}{50}\times 14$
$300.5+56=356.5$