Question

Find the mode for the following data $:$

Class interval	$0-2$	$2-4$	$4-6$	$6-8$	$8-10$
Frequency	$1$	$3$	$6$	$5$	$2$

• A. $5.2$
• B. $5.3$
• C. $5.4$
• D. $5.5$

Answer 1

The correct option is D $5.5$

Here frequency of class interval $4-6$ is maximum.

So, it is the modal class

Now $l$ = lower limit of modal class $=4$

$f_1=$ frequency of modal class $=6$

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

$f_2=$ frequency of class succeeding the modal class $=5$

$h=$ class interval width $=2$

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

$=4+\left(\frac{6-3}{2\times 6-3-5}\right)\times 2$

$=4+\left(\frac{3}{12-8}\right)\times 2$

$=4+1.5$

$=5.5$

Mode$=5.5$