Question

Find the median of the following numbers
(i) $24,22,23,14,15,7,21$
(ii) $17,15,9,13,21,32,42,7,12,10$.

Answer 1

(i) Let us arrange the numbers in ascending order as below.
$7,14,15,21,22,23,24$
Number of items $n=7$ is an odd number.
So, there exist only one middle term.
Thus, the Median $={\left(\frac{n+1}{2}\right)}^{th}$observation
$={\left(\frac{7+1}{2}\right)}^{th}$ observation
$=4^{th}$ observation $=21$

(ii) Let us arrange the numbers in ascending order
$7,9,10,12,13,15,17,21,32,42$.
Number of items $n=10$ is even number.
So, there exists two middle terms.
Thus, the median is the mean of ${\left(\frac{n}{2}\right)}^{th}$ and ${(\frac{n}{2}+1)}^{th}$ observations.
${\left(\frac{n}{2}\right)}^{th}$ observation $={\left(\frac{10}{2}\right)}^{th}$ observation $=5^{th}$ observation $=13$
${(\frac{n}{2}+1)}^{th}$ observation $(\frac{10}{2}+1)=(5+1)=6^{th}$ observation $=15$.
$\therefore$ Median $=\frac{13+15}{2}=\frac{28}{2}=14$