Question

If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be the _______ .

• A. upper limit of the modal class
• B. midpoint of the modal class
• C. midpoint of the preceding class
• D. lower limit of the modal class

Answer 1

The correct option is B midpoint of the modal class

The formula for the mode is as follows.

$Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

where $l=$ 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
$Mode=l+\left(\frac{f_1-f}{2f_1-f-f}\right)\times h$
$Mode=l+\left(\frac{f_1-f}{2(f_1-f)}\right)\times h$
$Mode=l+\frac{1}{2}\times h$,

But $h=u-l$

$\Rightarrow Mode=l+\frac{1}{2}(u-l)$

$\Rightarrow Mode=\frac{1}{2}(u+l)$
which is the midpoint of 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.