Question

The mode of the following frequency distribution is

Class	1-10	11-20	21-30	31-40	41-50
$f_i$	5	7	8	6	4

• A. $24$
• B. $23.83$
• C. $27.16$
• D. None of these

Answer 1

The correct option is B $23.83$

Frequency distribution table:

$ci$	$f_i$
$0.5-10.5$	$5$
$10.5-20.5$	$7\left(f_0\right)$
$20.5-30.5$	$8\left(f_1\right)$
$30.5-40.5$	$6\left(f_2\right)$
$40.5-50.5$	$4$

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

Here,

maximum frequency $f_1=8$

$\Rightarrow$ modal class $=20.5-30.5$

lower limit of modal class $l=20.5$

class size $h=10$

preceding frequency of modal class $f_0=7$

succeeding frequency of modal class $f_2=6$

$\therefore Mode=20.5+(\frac{8-7}{16-7-6})\times 10$

$\therefore Mode=20.5+(\frac{1}{3})\times 10$

$\therefore Mode=23.83$

Hence, option $B$ is correct.