Question

If Median = Mode + $x$ (Mean - Mode), then find the value of $x$.

• A. 3
• B. 2
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is D $\frac{2}{3}$

We know that,
Mode = 3 Median - 2 Mean
$\Rightarrow$ 3 Median = Mode + 2 Mean
$\Rightarrow \text{Median}=\frac{1}{3}\text{Mode}+\frac{2}{3}\text{Mean}$
On adding and subtracting $\frac{2}{3}\text{Mode}$ in RHS, we get:
$\text{Median}=\frac{1}{3}\text{Mode}+\frac{2}{3}\text{Mean}+\frac{2}{3}\text{Mode}-\frac{2}{3}\text{Mode}$
$=\text{Mode}+\frac{2}{3}\text{(Mean - Mode)}$

Therefore, $x=\frac{2}{3}$