Find the median of

Question:

Find the median of
(i) 17, 19, 32, 10, 22, 21, 9, 35
(ii) 72, 63, 29, 51, 35, 60, 55, 91, 85, 82
(iii) 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17, 27

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

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

$=16$

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