Question

In an arranged discrete series in which total number of observation $n$ are even, then median $n$ is :

• A. ${\left(\frac{n+1}{2}\right)}^{th}$ item (term)
• B. $\frac{n^{th}}{2}$ item (term)
• C. ${[\left(\frac{n+1}{2}\right)+1]}^{th}$ item (term)
• D. The average of $\frac{n^{th}}{2}$ and ${\left(\frac{n+3}{2}\right)}^{th}$ item (term)

Answer 1

The correct option is D The average of $\frac{n^{th}}{2}$ and ${\left(\frac{n+3}{2}\right)}^{th}$ item (term)

Given $n$ is even say $n=2m$ i.e.$=\frac{n}{2}$

Now there are two middle items which are ${\left(\frac{2m}{2}\right)}^{th}$ and ${(\frac{2m}{2}+1)}^{th}$
i.e $m^{th}$ and ${(m+1)}^{th}$ items

i.e ${\frac{n}{2}}^{th}$ and ${(\frac{n}{2}+1)}^{th}$ items $i.e{\left(\frac{n}{2}\right)}^{th}$ and${\left(\frac{n+3}{2}\right)}^{th}$ items

$\therefore$ Median is average of ${\left(\frac{n}{2}\right)}^{th}$ and ${\left(\frac{n+3}{2}\right)}^{th}$ item.