The mean of the following distribution is 50 but the frequency `f_(1) and f_(2)` in classes 20-40 and 60-80, resepectively are not known. Find these frequencies, if the sum of all the fequencies is 120

Explanation

First we calculate the class mark of given data

Given data sum of all frequencies =120
`Rightarrow sumf_(i)=68+f_(1)+f_(2)=120`
`Rightarrow f_(1)+f_(2)=52`
Here, assumed mean a=50
and (class width)h=20
By step deviation method `Mean=a+(sumf_(i)u_(i))/(sumf_(i))xxh`
`Rightarrow 50=50+(4+f_(2)-f_(1))/(120)xx20`
`Rightarrow 4+f_(2)-f_(1)=0`
`Rightarrow -f_(2)+f_(1)=4`
On adding Eq. (i) and (ii), we get 2f_(1)=56
`Rightarrow `f_(1)=24`
`f_(2)=24`
Hence, `f_(1)=28 and f_(2)=24`