#### The mean of the following frequency distribution is 50, but the frequencies f1 and f2 in classes 20-40 and 60-80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120. Class 0-20 20-40 40-60 60-80 80-100 Frequency 17 fi 32 f2 19

Solution.

 Class (fi) xi $\mu _{c}= \frac{\left ( x_{i}-a \right )}{h}$ fi$\mu _{i}$ 0-20 17 10 -2 -34 20-40 f1 30 -1 -f1 40-60 32 50=a 0 0 60-80 f2 70 1 f2 80-100 19 90 2 38 $\sum f_{i}= 68+f_{i}+f_{2}$

Sum of all frequencies = 120
$\Rightarrow$68 + f1 + f2 = 120
f1 + f2 = 52                  …(1)
a = 50, h = 20
mean = $a+\frac{\sum f_{i}{\mu _{i}}}{\sum f_{i}}\times h$
50= 50 +  $\frac{\left ( 4+f_{2}-f_{1} \right )\times 20}{20}$
0= (4 + f2 – f1)
–f2 + f1 = 4                  …(2)
add (1) and (2) we get
2f1 = 56  $\Rightarrow f_{1}= 28$
Put f1 = 28 in equation (1)
f2 = 52 – 28  $\Rightarrow f_{2}= 24$