Question

Calculate the median from the following data:

Marks below:	10	20	30	40	50	60	70	80
No. of students:	15	35	60	84	96	127	198	250

Answer 1

Marks below	No of students	Class interval	Frequency	Cumulative frequency
10	15	0 - 10	15	15
20	35	10 - 20	20	35
30	60	20 - 30	25	60
40	84	30 - 40	24	84
50	96	40 - 50	12	96
60	127	50 - 60	37	127
70	198	60 - 70	71	198
80	250	70 - 80	52	250
			N = 250

Here, N = 250

So, N/2 = 125

Thus, the cumulative frequency just greater than 125 is 127 and the corresponding class is 50 - 60.

Therefore, 50 - 60 is the median class.

Here, l = 50, f = 31, F = 96 and h = 10

We know that

Median `=l+{(N/2-F)/f}xxh`

`=50+{(125-96)/31}xx10`

`=50+(29xx10)/31`

`=50+290/31`

= 50 + 9.35

= 59.35

Hence, the median is 59.35.