Question

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 1.46.

Number of accidents (x):	0	1	2	3	4	5	Total
Frequency (f):	46	?	?	25	10	5	200

Answer 1

Let the missing frequencies be $f_1$ and $f_2$.
Computation of Arithmetic Mean

$x_i$	$f_i$	$f_i{x}_i$
$0$	$46$	$0$
$1$	$f_1$	$f_1$
$2$	$f_2$	$2f_2$
$3$	$25$	$75$
$4$	$10$	$40$
$5$	$5$	$25$

$N=86+f_1+f_2$

$\sum f_i{x}_i=140+f_1+2f_2$

We have ,
$N=200\Rightarrow 200=86+f_1+f_2\Rightarrow f_1+f_2=114$ ..... (i)
Also,
Mean = 1.46

$\Rightarrow 1.46=\frac{\sum f_i{x}_i}{N}$

$\Rightarrow 1.46=\frac{140+f_1+2f_2}{200}$

$\Rightarrow 292=140+f_1+2f_2\Rightarrow f_1+2f_2=152$ ....(ii)
Solving equation (i) and (ii), we get
$f_1=76$ and $f_2=38$