Find the median of

Solution:

(i) Arranging the numbers in ascending order, we get:
9, 10, 17, 19, 21, 22, 32, 35
Here, n is 8, which is an even number.
If n is an even number, we have:

Median $=$ Mean of $\left(\frac{n}{2}\right)$ th $\&\left(\frac{n}{2}+1\right)$ th observations

Now,

Median $=$ Mean of $\left(\frac{8}{2}\right)$ th \& $\left(\frac{8}{2}+1\right)$ th observations

$=$ Mean of the 4 th \& 5 th observations

$=\frac{1}{2}(19+21)$

$=20$

(ii) Arranging the numbers in ascending order, we get:
29, 35, 51, 55, 60, 63, 72, 82, 85, 91
Here, n is 10, which is an even number.
If n is an even number, we have:

Median $=$ Mean of $\left(\frac{n}{2}\right)$ th $\&\left(\frac{n}{2}+1\right)$ th observations

Now,

Median $=$ Mean of $\left(\frac{10}{2}\right)$ th $\&\left(\frac{10}{2}+1\right)$ th observations

$=$ Mean of the 5 th \& 6 th observations

$=\frac{1}{2}(60+63)$

$=61.5$

(iii) Arranging the numbers in ascending order, we get:
3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81
Here, n is 12, which is an even number.
If n is an even number, we have:

Median $=$ Mean of $\left(\frac{n}{2}\right)$ th \& $\left(\frac{n}{2}+1\right)$ th observations

Now,

Median $=$ Mean of $\left(\frac{12}{2}\right)$ th $\&\left(\frac{12}{2}+1\right)$ th observations

$=$ Mean of the 6 th \& 7 th observations

$=\frac{1}{2}(15+17)$

$=16$