Question

The following table shows the marks obtained by 100 students of class x in a school during a particular academic session. Find the mode of this distribution.

Marks	No. of students
Less than 10	7
Less than 20	21
Less than 30	34
Less than 40	46
Less than 50	66
Less than 60	77
Less than 70	92
Less than 80	100

• A. $44.71$
• B. $48.35$
• C. $51.65$
• D. $57.22$

Answer 1

The correct option is A $44.71$

Frequency distribution table:

$ci$	$f_i$	$cf$
$0-10$	$7$	$7$
$10-20$	$21-7=14$	$21$
$20-30$	$34-21=13$	$34$
$30-40$	$46-24=12$	$46$
$40-50$	$66-46=20$	$66$
$50-60$	$77-66=11$	$77$
$60-70$	$92-77=15$	$92$
$70-80$	$100-92=8$	$100$

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

Here,

maximum frequency $f_1=20$

$\Rightarrow$ modal class $=40-60$

lower limit of modal class $l=40$

class size $h=10$

preceding frequency of modal class $f_0=12$

succeeding frequency of modal class $f_2=11$

$\therefore Mode=40+(\frac{20-12}{40-12--11})\times 10$

$\therefore Mode=40+(\frac{8}{17})\times 10$

$\therefore Mode=44.705\approx 44.71$

Hence, option $A$ is correct.