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Find the values of frequencies x and y in the following frequency distribution table, if N=100 and median is 32.

Marks: 0-10 10-20 20-30 30-40 40-50 50-60 Total
No. of Students: 10 x 25 30 y 10 100

 

 

 

 

 

 

 
 
 
 
 

Answers (1)

Marks 0-10 10-20 20-30 30-40 40-50 50-60 Total
No. of students 10 x 25 30 y 10 100
cumulative freq. 10 10+x 10+25+x=35+x

30+35+x

=65+x

65+x+y

65+x+y+10

+75+x+y

 

N=100=\sum f

M=32

Now, 75+x+y=100

            \Rightarrow x+y=25 _____(a)

As the median is 32 , it must lie in the period 30-40

\Rightarrow f=30

       c=10

     c.f=35+x

        L=30

Median (M) =

 L+\frac{\left ( \frac{N}{2}-C.F \right )}{f}\times c

        32=30+\left ( \frac{\frac{100}{2}-35-x}{30} \right )\times 10

          32-30=\frac{15-x}{3}

                6=15-x

                \Rightarrow x=9

Now from eq (a)

        9+y=25

            y=16

Posted by

Safeer PP

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