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

            

Answers (1)

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 
\Rightarrow68 + 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

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