Question

Calculate the median from the following frequency distribution table:

Class	5 – 10	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40	40 – 45
Frequency	5	6	15	10	5	4	2	2

 

Answer 1

Class	Frequency (f)	Cumulative Frequency (cf)
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

Now, N = 49
`⇒ N/2` = 24.5.
The cumulative frequency just greater than 24.5 is 26 and the corresponding class is 15 - 20.
Thus, the median class is 15 – 20.
∴ l = 15, h = 5, f = 15, cf = c.f. of preceding class = 11 and `N/2` = 24.5.
Now,
Median, M = `l + {h×((N/2−cf)/f)}`
                   `= 15 + {5 × ((24.5 − 11)/15)}`      

                    = 15 + 4.5
                    = 19.5
     Hence, the median = 19.5.