Question

Find the median of
(i) 2, 10, 9, 9, 5, 2, 3, 7, 11
(ii) 15, 6, 16, 8, 22, 21, 9, 18, 25
(iii) 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22
(iv) 7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2

Answer 1

(i) Arranging the numbers in ascending order, we get:
2, 2, 3, 5, 7, 9, 9, 10, 11
Here, n is 9, which is an odd number.
If n is an odd number, we have:
$\mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{n+1}{2}\right)\mathrm{th}\mathrm{observation}$
Now,
$$\begin{gathered} \mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{9+1}{2}\right)\mathrm{th}\mathrm{observation} \\ =\mathrm{Value}\mathrm{of}\mathrm{the}5\mathrm{th}\mathrm{observation} \\ =7 \end{gathered}$$

(ii) Arranging the numbers in ascending order, we get:
6, 8, 9, 15, 16, 18, 21, 22, 25
Here, n is 9, which is an odd number.
If n is an odd number, we have:
$\mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{n+1}{2}\right)\mathrm{th}\mathrm{observation}$
Now,
$$\begin{gathered} \mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{9+1}{2}\right)\mathrm{th}\mathrm{observation} \\ =\mathrm{Value}\mathrm{of}\mathrm{the}5\mathrm{th}\mathrm{observation} \\ =16 \end{gathered}$$

(iii) Arranging the numbers in ascending order, we get:
6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25
Here, n is 11, which is an odd number.
If n is an odd number, we have:
$\mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{n+1}{2}\right)\mathrm{th}\mathrm{observation}$
Now,
$$\begin{gathered} \mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{11+1}{2}\right)\mathrm{th}\mathrm{observation} \\ =\mathrm{Value}\mathrm{of}\mathrm{the}6\mathrm{th}\mathrm{observation} \\ =16 \end{gathered}$$

(iv) Arranging the numbers in ascending order, we get:
0, 1, 2, 2, 3, 4, 4, 5, 5, 7, 8, 9, 10
Here, n is 13, which is an odd number.
If n is an odd number, we have:
$\mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{n+1}{2}\right)\mathrm{th}\mathrm{observation}$
Now,
$$\begin{gathered} \mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{13+1}{2}\right)\mathrm{th}\mathrm{observation} \\ =\mathrm{Value}\mathrm{of}\mathrm{the}7\mathrm{th}\mathrm{observation} \\ =4 \end{gathered}$$