Question

Class	$65-85$	$85-105$	$105-125$	$125-145$	$145-165$	$165-185$	$185-205$
Frequency	$4$	$15$	$3$	$20$	$14$	$7$	$14$

Let us find the difference between upper class limit in median class and lower class limit of modal class of the frequency distribution table.

Answer 1

$Class$	$Frequency$	$c.f$
$65-85$	$4$	$4$
$85-105$	$15$	$4+15=19$
$105-125$	$3$	$19+3=22$
$125-145$	$20$	$22+20=42$
$145-165$	$14$	$42+14=56$
$165-185$	$7$	$56+7=63$
$185-205$	$14$	$63+14=77$
	$n=77$

$\Rightarrow$ Median class $={\left(\frac{n+1}{2}\right)}^{th}position={\left(\frac{77+1}{2}\right)}^{th}={39}^{th}position$

$\Rightarrow$ $39$ nearest to $c.f$ $42$.

$\therefore$ Median class $=125-145$

$\Rightarrow$ In table we can see, class $125-145$ has highest frequency $20$

$\therefore$ Modal class $=125-145$

We can see, both median class and modal class are same.

$\Rightarrow$ So, required difference $=145-125=20$