Question

Calculate the median from the following frequency distribution:
$\begin{array}{ccccccccc}\text{Class}& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40& 40-45\\ \text{Frequency}& 5& 6& 15& 10& 5& 4& 2& 2\end{array}$

Answer 1

We prepare the cumulative frequency table, as shown:

Class	Frequency (f)	Cumulative frequency
5-10	5	5
10-15	6	11
15-20	15	26
20-25	10	36
25-30	5	41
30-35	4	45
35-40	2	47
40-45	2	49
	N=Σf=49

N= 49

⇒N/2=24.5

The cumulative frequency greater than 24.5 is 26 and the corresponding class is 15-20.

Thus the median class is 15-20.

Therefore, l= 15, h = 5,
f = 15,
c.f. of preceding class = 11 and N/2=24.5

Median,
M=l+((N/2−cf)/f)×h

Median=15+(24.5–11/15)×5


Median=15+4.5

Median=19.5

Hence, median is 19.5 .