Question

Find the approximate value of mode for the following data $:$

Class interval	$7-14$	$14-21$	$21-28$	$28-35$	$35-42$
Frequency	$2$	$4$	$3$	$10$	$1$

• A. $30$
• B. $32$
• C. $31$
• D. $35$

Answer 1

The correct option is C $31$

Here frequency of class interval $28-35$ is maximum.

So, it is the modal class

Now $l$ = lower limit of modal class $=28$

$f_1=$ frequency of modal class $=10$

$f_0=$frequency of class preceding the modal class $=3$

$f_2=$ frequency of class succeeding the modal class $=1$

$h=$ class interval width $=7$

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

$=28+\left(\frac{10-3}{2\times 10-3-1}\right)\times 7$

$=28+\left(\frac{7}{20-4}\right)\times 7$

$=28+3.0625$

$=31.06$

Mode$\sim 31$