Question

Find mode for the following data$:$

Size	$2-5$	$5-8$	$8-11$	$11-14$
Number of shoes	$1$	$4$	$8$	$7$

• A. $10.4$
• B. $11.4$
• C. $12.4$
• D. $13.4$

Answer 1

The correct option is A $10.4$

Here frequency of class interval $8-11$ is maximum.

So, it is the modal class

Now $l$ = lower limit of modal class $=8$

$f_1=$ frequency of modal class $=8$

$f_0=$ frequency of class preceding the modal class $=4$

$f_2=$ frequency of class succeeding the modal class $=7$

$h=$ class interval width $=3$

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

$=8+\left(\frac{8-4}{2\times 8-4-7}\right)\times 3$

$=8+\left(\frac{4}{16-11}\right)\times 3$

$=8+2.4$

$=10.4$

Mode$=10.4$