Question

Find out median:
(a)

Serial No.	1	2	3	4	5	6	7	8	9
Values	2	4	10	8	15	20	12	25	30

(b)

X	5	10	15	20	25
f	2	4	10	8	15

Answer 1

(a) For the calculation of median the given values are first arranged in ascending order as follows.

Serial Number	Values	Ascending Order
1 2 3 4 5 6 7 8 9	2 4 10 8 15 20 12 25 30	2 4 8 10 12 15 20 25 30

Here, N = 9
$$\begin{gathered} \mathrm{Median}=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ ={\left(\frac{9+1}{2}\right)}^{\mathrm{th}} \\ =5^{\mathrm{th}}\mathrm{item} \\ =12 \end{gathered}$$
Thus, median is 12.

(b)

X	f	c.f
5	2	2
10	4	6
15	6	12
20	8	20
25	10	30

$$\begin{gathered} \mathrm{Median}=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{30+1}{2}\right)}^{\mathrm{th}} \\ =\mathrm{Size}\mathrm{of}15.5^{\mathrm{th}}\mathrm{item} \end{gathered}$$
Now, we need to look at the column of cumulative frequency. The item just exceeding the 15.5^th item is 20, which corresponds to 20.
Thus, median is 20.