Question

If the median and mean of a given data are $\frac{1}{x}$ and $\frac{1}{y}$ respectively, then its mode is

• A. $\frac{3y-2x}{xy}$
• B. $\frac{3y+2x}{xy}$
• C. $\frac{x+y}{2xy}$
• D. $\frac{y-2x}{3xy}$

Answer 1

The correct option is A $\frac{3y-2x}{xy}$

Median $=\frac{1}{x}$ and Mean $=\frac{1}{y}$
Using empirical relationship between the three measure of central tendency:
3Median = Mode + 2Mean
$\Rightarrow$ Mode = 3Median – 2Mean
$=\frac{3}{x}-\frac{2}{y}$
$=\frac{3y-2x}{xy}$
Hence, the correct answer is option (1).