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  • 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.

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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