Question

The median of the following distribution is

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Number of students	8	7	13	12	30	25

• A. 42.5
• B. 43.4
• C. 45
• D. 47.2

Answer 1

The correct option is A 42.5

Marks	$x_i$	$f_i$	cf
0-10 10-20 20-30 30-40 40-50 50-60	5 15 25 35 45 55	8 7 13 12 30 25	8 15 28 40 70 95

Here, the total number of observations (N) is 95.
$\therefore \frac{N}{2}=\frac{95}{2}=47.5$
This observation lies in the interval 40 - 50.
Here,
Lower limit, (l) = 40
Cumulative frequency of class preceding the median class, (cf) = 40
Frequency of the median class (f) = 30
Class size (h) = 10
$\therefore Median=l+\left(\frac{\frac{N}{2}-cf}{f}\right)\times h$
$=40+\left(\frac{47.5-40}{30}\right)\times 10$
$=40+\frac{7.5}{3}$
$=40+2.5$
$=42.5$
Hence, the correct answer is option a.