Question

Find the median from the following data:
$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{Below 10}& 12\\ \text{Below 20}& 32\\ \text{Below 30}& 57\\ \text{Below 40}& 80\\ \text{Below 50}& 92\\ \text{Below 60}& 116\\ \text{Below 70}& 164\\ \text{Below 80}& 200\end{array}$

Answer 1

Sol:

The given series is of inclusive form. Converting it into exclusive form and preparing the cumulative frequency table, we get

Marks	Frequency fi	C.F
0-10	12	12
10-20	20	32
20-30	25	57
30-40	23	80
40-50	12	92
50-60	24	116
60-70	24	116
70-80	36	200
	N=∑fi=200

N =200

=> N/2 = 100

Now,

The cumulative frequency just greater than 100 is 116 and corresponding class is 50-60.

Thus, the median class is 50-60

I = 50, h = 10, f = 24, c = C.F. preceding median class = 92 and N/2 = 100

Median = I+[h×(N/2−c)/f]=50+[10×(100−92)/24]

=50+[10×84/24]=50+[10×84/24]

= 50 + 3.33 = 53.33

Hence, Median = 53.33