The mean of the following frequency distribution


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.


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


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

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


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