# Find the median of

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

Solution:

(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:

Median $=$ Value of $\left(\frac{n+1}{2}\right)$ th observation

Now,

Median $=$ Value of $\left(\frac{9+1}{2}\right)$ th observation

$=$ Value of the 5 th observation

$=7$

(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:

Median $=$ Value of $\left(\frac{n+1}{2}\right)$ th observation

Now,

Median $=$ Value of $\left(\frac{9+1}{2}\right)$ th observation

$=$ Value of the 5 th observation

$=16$

(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:

Median $=$ Value of $\left(\frac{n+1}{2}\right)$ th observation

Now,

Median $=$ Value of $\left(\frac{11+1}{2}\right)$ th observation

$=$ Value of the 7 th observation

$=4$