Question

Find the median from the following data:

Marks	No of students
Below 10	12
Below 20	32
Below 30	57
Below 40	80
Below 50	92
Below 60	116
Below 70	164
Below 80	200

Answer 1

Class	frequency (f)	cumulative frequency (f)
0 – 10	12	12
10 – 20	32	(32 - 12) = 20
20 – 30	57	(57 - 32) = 25
30 – 40	80	(80 - 57) = 23
40 – 50	92	(92 - 80) =12
50 – 60	116	(116 - 92) = 24
60 – 70	164	(164 - 116) = 48
70 – 80	200	(200 - 164) = 36
		N = Σ𝑓 = 200

Now, N = 200
`⇒ N/2 = 100`.

The cumulative frequency just greater than 100 is 116 and the corresponding class is 50 – 60.
Thus, the median class is 50 – 60.
∴ l = 50, h = 10, f = 24, cf = c.f. of preceding class = 92 and `N/2` = 100.
∴ Median, `M = l + {h×((N/2−cf)/f)}`
             `= 50 + {10× ((100 − 92)/24)}`
             = 50 + 3.33
            = 53.33
Hence, median = 53.33.