# The mean of the following frequency distribution

Question:

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.

Solution:

First we caluculate the class mark of given data

Given that, sum of all frequencies $=120$

$\Rightarrow \quad \Sigma f_{1}=68+f_{1}+f_{2}=120$

$\Rightarrow \quad f_{1}+f_{2}=52$ $\ldots(\mathrm{i})$

Here, $\quad$ (assumed mean) $a=50$

and (class width) $h=20$

By step deviation method,

Mean $=a+\frac{\Sigma f_{i} u_{l}}{\Sigma f_{j}} \times h$

$\Rightarrow$ $50=50+\frac{\left(4+t_{2}-f_{12}\right.}{120} \times 20$

$\Rightarrow \quad 4+t_{2}-t_{1}=0$

$\Rightarrow \quad-f_{2}+f_{1}=4$ ...(ii)

On adding Eqs. (i) and (ii), we get

$2 f_{1}=56$

$\Rightarrow \quad f_{1}=28$

Put the value of $f_{1}$ in Eq. (i), we get

$f_{2}=52-28$

$\Rightarrow \quad f_{2}=24$

Hence, $f_{1}=28$ and $f_{2}=24$

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