Question

Find the median from the following data: $\begin{array}{cccccccccc}{x}_i& 5& 10& 15& 20& 25& 30& 35& 40& 45\\ \text{Frequency (}{f}_i\text{)}& 7& 10& 16& 32& 24& 16& 11& 5& 2\end{array}$

• A.
  15
• B.
  20
• C.
  25
• D.
  30

Answer 1

The correct option is B

20

$x_i$	$f_i$	C.F
5	7	7
10	10	17
15	16	33
20	32	65
25	24	89
30	16	105
35	11	116
40	5	121
45	2	123
	N = ∑$f_i$ =123

Here N = 123 (which is odd )
=> (N+1)/2 = 62
So the median will be the ${62}^{nd}$ observation.
From the table, we can conclude that the ${62}^{nd}$ observation corresponds to 20.
Hence, the median of the given data is 20.