For a grouped frequency distribution mean is 60. If the number of observations in each class interval be doubled, what will be the new mean?

Answer :

We know in grouped frequency distribution , Mean  = $\frac{{\sum }_{}fx}{{\sum }_{}f}$

Here f =  Frequency
and
x  =  Mid point of the group .

Given :  Mean of a grouped frequency distribution = 60 , So

$\frac{{\sum }_{}fx}{{\sum }_{}f}$ = 60 

Now  the number of observations in each class interval be doubled . So

New frequency  =  2 f
So,
New mean  = $\frac{{\sum }_{}2fx}{{\sum }_{}2f} = \frac{2{\sum }_{}fx}{2{\sum }_{}f} = \frac{{\sum }_{}fx}{{\sum }_{}f}$ = 60                                                          ( Ans )