Question

If the difference between mean and mode is $63$, then the difference between mean and median can be

• A. $189$
• B. $21$
• C. $31$
• D. $48$

Answer 1

The correct option is B $21$

Given : $\text{Mean}-\text{Mode}=\pm 63$
Using,
$\text{Mode}=3\text{Median}-2\text{Mean}-\text{Mode}=2\text{Mean}-3\text{Median}$
Now adding $\text{Mean}$ to both sides,
$\text{Mean}-\text{Mode}=3(\text{Mean}-\text{Median})\cdots \left(i\right)$
Given:
$\text{Mean}-\text{Mode}=\pm 63$
From $\left(i\right)$
$\Rightarrow \text{Mean}-\text{Median}=\pm \frac{63}{3}=\pm 21$
From the given options, the required difference can be $21.$