Question

The relation between mean, median, and mode is

• A. $\mathrm{Mode}=3\left(\mathrm{Median}\right)-2\left(\mathrm{Mean}\right)$
• B. $\mathrm{Mode}=2\left(\mathrm{Median}\right)-3\left(\mathrm{Mean}\right)$
• C. $\mathrm{Mode}=3\left(\mathrm{Mean}\right)-2\left(\mathrm{Median}\right)$
• D. $\mathrm{Mode}=2\left(\mathrm{Mean}\right)-3\left(\mathrm{Median}\right)$

Answer 1

The correct option is A

$\mathrm{Mode}=3\left(\mathrm{Median}\right)-2\left(\mathrm{Mean}\right)$

According to the given question,

The empirical relationship between mean, mode, and the median is given as

Mean$-$Mode $=$ $3$(Mean $-$ Median)

Simplify the above equation,

Mean$-$ Mode$=$ $3$Mean $-$ $3$Median

$-$Mode $=$ $3$Mean $-$ $3$Median $-$ Mean

$-$Mode $=$ $2$Mean $-$ $3$Median

Mode $=$ $3$Median $-$ $2$Mean

Hence, the option$\left(A\right)$ is the correct option.