Question

Find the median of the following data.

Maths marks	$60-65$	$65-70$	$70-75$	$75-80$	$80-85$	$85-90$	$90-95$
No. of students	$8$	$12$	$14$	$8$	$5$	$6$	$4$

• A. $73.05$
• B. $72.54$
• C. $63.54$
• D. $91.09$

Answer 1

The correct option is A $73.05$

Converting the given data into a frequency distribution table

Maths marks	No. of students (f)	c.f.
$60-65$	$8$	$8$
$65-70$	$12$	$20$
$70-75$	$14$	$34$
$75-80$	$8$	$42$
$80-85$	$5$	$47$
$85-90$	$6$	$53$
$90-95$	$4$	$57$
	$\text{N}=\Sigma \text{f}=57$

Here, $\text{N=57}$

$⟹\frac{N}{2}=\frac{57}{2}=28.5$

$⟹$In the above table $70-75$ is the median class and the respective c.f. is $20$ (cumulative frequency of the class preceding the median class)

Acc to ques,

$l=70$ (lower limit of median class)

c.f. $=20$

$h=l_2-l_1=5$ (width of class interval of median class)

$f=14$ (frequency of median class)

$\text{Median}=l+\frac{\frac{N}{2}-c.f.}{f}\times h=70+\frac{28.5-20}{14}\times 5$

$⟹$ Median $=73.05$