Question

Frequency distribution of daily commission received by $100$ salesmen is given.

Daily Commission(in Rs.)	No. of Salesmen
$100-120$	$20$
$120-140$	$45$
$140-160$	$22$
$160-180$	$09$
$180-200$	$04$

Find mean daily commission received by salesman, by assumed mean method.

Answer 1

Let us take the assumed mean to be $A=150$.

$Interval$	$x_i$	$f_i$	$d_i=x_i-A$	$f_i{d}_i$
$100-120$	$110$	$20$	$-40$	$-800$
$120-140$	$130$	$45$	$-20$	$-900$
$140-160$	$150$	$22$	$0$	$0$
$160-180$	$170$	$09$	$20$	$180$
$180-200$	$190$	$04$	$40$	$160$
$Total$		$\sum f_i$ = $100$		$\sum f_i{d}_i$ $=-1360$

Now the actual mean by the assumed mean method is given by,

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

where $\overline{x}$ is the actual mean and $A$ is the assumed mean.

Substituting the values into the formula, we get:

$\overline{x}=150+\frac{(-1360)}{100}$

That gives, $\overline{x}=136.4$. The mean daily commission is $Rs136.4$