Question

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 1

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 )