Question

Find mode for grouped data given below$:$

X	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
F	$20$	$10$	$10$	$10$	$40$	$30$

• A. $57.5$
• B. $67.5$
• C. $87.5$
• D. $97.5$

Answer 1

The correct option is B $67.5$

Here frequency of class interval $60-70$ is maximum.

So, it is the modal class

Now,$l=$ lower limit of modal class

$=60$

$f_1=$ frequency of modal class

$=40$

$f_0=$ frequency of class preceding the
modal class

$=10$

$f_2=$ frequency of class succeeding the

modal class

$=30$

$h=$ class interval width

$=10$

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

$=60+\left(\frac{40-10}{2\times 40-10-30}\right)\times 10$

$=60+\left(\frac{30}{80-40}\right)\times 10$

$=60+7.5$

$=67.5$

Mode$=67.5$