Question

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

Answer 1

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`