Question

If mean : median of a certain data is $2:3$, what is the ratio of its mode and mean?

• A. $3:2$
• B. $5:2$
• C. $3:5$
• D. $2:3$

Answer 1

The correct option is B $5:2$

$\frac{mean}{median}=\frac{2}{3}\frac{mode}{mean}=?Since,mode=3median-2meanmean-mode=3(mean-median)mean(1-\frac{mode}{mean})=3mean(1-\frac{median}{mean})\Rightarrow 1-\frac{mode}{mean}=3(1-\frac{3}{2})\Rightarrow 1-\frac{mode}{mean}=-\frac{3}{2}\Rightarrow 1+\frac{3}{2}=\frac{mode}{mean}$

Therefore, $\frac{mode}{mean}=\frac{5}{2}$