Find the missing frequencies f1 and f2 in the following frequency distribution table, if N=100 and the median is 32.

Given the following frequency distribution table in which the median of data is 32 and

N = 100

From the table it is clear that N = 100 and median is 32, therefore corresponding median class is 30-40.
Therefore,

l = 30, F = 30, cf = 35 + f_{1}, and h = 10

Median = l + (\frac{\frac{N}{2} - cf}{F}) \times h

\Rightarrow 32 = 30 + (\frac{\frac{100}{2} - 35 - f_{1}}{30}) \times 10

\Rightarrow 2 \times 3 = (50 - 35 - f_{1})

\Rightarrow 6 = (15 - f_{1})

\Rightarrow f_{1} = 9

Also the sum of frequency is 100.
Form an equation using this.

75 + f_{1} + f_{2} = 100

{\Rightarrow f}_{1} + f_{2} = 100 - 75

{\Rightarrow f}_{1} + f_{2} = 25

……………(1)
Substitute value of

f_{1}

in equation 1 to calculate value of

f_{2}

9 + f_{2} = 25

{\Rightarrow f}_{2} = 25 - 9

{\Rightarrow f}_{2} = 16

Thus, the value of

f_{1} = 9

and that of

f_{2} = 16

.
Hence, option 3 is correct.

Find the missing frequencies $f_{1}$ and $f_{2}$ in the following frequency distribution table, if $N = 100$ and the median is 32.