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

140 Kg 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 (F)
60	127	50 - 60	31 (f)	127
70	198	60 - 70	71	198
80	250	70 - 80	52	250
			N = 250

We have, 

N = 250

\(\frac{N}{2}=\frac{250}{2}=125\)

The cumulative frequency is just greater than \(\frac{N}{2}\) is 127 then median class is 50-60 such that:

l = 50, f = 31, F = 96, h = 60-50 = 10

Median = I + \(\frac{\frac{N}{2}-F}{f}\)

\(=50+\frac{125-96}{31}\times 10\)

\(=50+\frac{29\times10}{31}\)

\(=\frac{445}{31}=59.35\)