Question

Find mode for the following data$:$

$X$	$2-4$	$4-6$	$6-8$	$8-10$	$10-12$	$12-14$	$14-16$
$F$	$1$	$2$	$2$	$3$	$6$	$3$	$2$

• A. $11$
• B. $12$
• C. $13$
• D. $14$

Answer 1

The correct option is A $11$

Here frequency of class interval $10-12$ is maximum.

So, the modal class is $10-12$

Now $l$ = lower limit of modal class $=10$

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

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

$f_2=$ frequency of class succeeding the modal class $=3$

$h=$ class width $=2$

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

$=10+\left(\frac{6-3}{2\times 6-3-3}\right)\times 2$

$=10+\left(\frac{3}{12-6}\right)\times 2$

$=10+\left(\frac{3}{6}\right)\times 2$

$=10+1$

$=11$

Hence, mode of the given frequency distribution is $11$