Answer: Option A
:
A
The formula for the mode is as follows.
$Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$
$l=$ lower boundary of the modal class
$h=$ size of the modal class interval
$f_1=$ frequency of the modal class.
$f_0=$ frequency of the class preceding the modal class
$f_2=$frequency of the class succeeding the modal class
If the preceding and succeeding classes have the same frequency, then $f_0=f_2=f\left(say\right)$.
Then the equation reduces to
$Mode=l+\left(\frac{f_1-f}{2f_1-f-f}\right)\times h$
$Mode=l+\left(\frac{f_1-f}{2(f_1-f)}\right)\times h$
$Mode=l+\frac{1}{2}\times h$, which is the midpointof the modal class.
$\therefore$If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be at the midpoint of the modal class.