Question

How can we find mode if two classes have the highest and same frequency? How can we identify the median class if two classes are equally near to $\frac{n}{2}$?

Answer 1

If there are more than one class intervals which have the same frequency (equally qualifying to be the mode class) then both of the classes will be the mode class. this is called bimodal.
However to calculate the mode of grouped data use the following formula
Mode $=L+\frac{(F-F_1)}{(F-F_1)+(F-F_2)}\times h$
where
$L=$ Lower limit of the modal class
$F=$ Frequency of the modal class
$F_1=$ Frequency of the class immediately previous of modal class
$F_2=$ Frequency of the class immediate next of modal class
$h=$ Range of the modal class (higher limit - lower limit)

The class interval whose cumulative frequency is greater than $\frac{N}{2},$ will be considered as median class.

For example:

$30-40$ $6$

$40-50$ $8$

$50-60$ $10$

If $\frac{N}{2}$ is $8,$ then median class is $50-60$