Question

There are 2 sets of numbers in increasing order. The first set has ‘n’ numbers where ‘n’ is an odd number. The 2nd set has ‘m’ numbers where ‘m’ is an even number. The medians for both of the sets respectively is ______.

• A. $\frac{(n+1)}{2}$${}^{th}$ term, $\text{average of}\left(\frac{m}{2}{)}^{th}and\right(\frac{m}{2}+1{)}^{th}\text{terms}$
• B. $\frac{n}{2}$${}^{th}$ term, $\text{average of}\left(\frac{m}{2}{)}^{th}and\right(\frac{m}{2}+1{)}^{th}\text{terms}$
• C. $\frac{n+1}{2}$${}^{th}$ term, $\left(\frac{m}{2}\right)$${}^{th}$ term
• D. Insufficient data

Answer 1

The correct option is A $\frac{(n+1)}{2}$${}^{th}$ term, $\text{average of}\left(\frac{m}{2}{)}^{th}and\right(\frac{m}{2}+1{)}^{th}\text{terms}$

Given that the data in the sets are arranged in ascending order.

When the observations are arranged in ascending or descending order, the median is the middile most observation.

For the first set: n is odd.
So, the median is (${\frac{n+1}{2}}^{th}$) term .

For the second set: m is even.
So, the median will be the average of the ${\frac{m}{2}}^{th}$ and the ${(\frac{m}{2}+1)}^{th}$observation.