Question

Find the median from the following data: $\begin{array}{cccccccccc}\text{Class}& 1-5& 6-10& 11-15& 16-20& 21-25& 26-30& 31-35& 36-40& 41-45\\ \text{Frequency}& 7& 10& 16& 32& 24& 16& 11& 5& 2\end{array}$

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
0.5-5.5	7	7
5.5-10.5	10	17
10.5-15.5	16	33
15.5-20.5	32	65
20.5-25.5	24	89
25.5-30.5	16	105
30.5-35.5	11	116
35.5-40.5	5	121
40.5-45.5	2	123
	N=∑fi=123

N =123

=> N/2 = 61.5

Now,

The cumulative frequency just greater than 61.5 is 65 and corresponding class is 15.5-20.5.

Thus, the median class is 15.5-20.5

I = 15.5, h = 5, f = 32, c = C.F. preceding median class = 33 and N/2 = 61.5

Median = I+[h×(N/2−c)/f]=15.5+[5×(61.5−33)/32]

= 15.5+4.45 = 19.95

Hence, median = 19.95