The frequency distributions of the weekly wages of some labourers of an industry are given below :

The number of labourers having Rs. 25 weekly wages is unknown. But it is known that the average weekly wages of a labourer is Rs. 27.50 . Find the unknown frequency .

Explanation

Here , assuming 30 as the origin and the class length 5 as the unit of degree, we get , the new variable mu, where `u=(x-30)/(5)`, i.e. `x-30+5 baru`
Let the unknown frequency be f. Then we prepare the following table :

`therefore baru=(sum uxx f)/(sumf )=(-17-f)/(52+f) and bar x =30+5 (-17-f)/(52+f)`
or `27.5 =30+5(-17-f)/(52+f) [ because x = Rs. 27.5]`
or , `-0.5 =-(17+f)/(52+f)` or , `0.5(52+f)=17+f ` or `26+0.5f=17+f`
or `26-17=f-0.5f `, or `9=0.5f` or , `f=18` , which is the required frequency.