Question

Consider the data :

Class	Frequency
$65-85$	$4$
$85-105$	$5$
$105-25$	$13$
$125-145$	$20$
$145-165$	$14$
$165-185$	$7$
$185-205$	$4$

The difference of the upper limit of the median class and the lower limit of the modal class is:

• A. $0$
• B. $19$
• C. $20$
• D. $38$

Answer 1

The correct option is C $20$

Answer:- The cumulative frequency table is:

Class	Frequency	Cumulative Frequency
65-85	4	4
85-105	5	9
105-125	13	22
125-145	20	42
145-165	14	56
165-185	7	63
185-205	4	67

Here, $\frac{N}{2}=\frac{67}{2}=33.5$

$\therefore$ Median class is "$125-145$."

$\Rightarrow$ Upper limit of median class is $145$.

Modal class = class with maximum frequency

Therefore modal class is "$125-145$."

$\Rightarrow$ Lower limit of modal class is $125$.

$\therefore$ difference of upper limit of median class and lower limit of modal class = $145-125=20$