Question

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

• 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,
$\text{Mean}-\text{Mode}=3\left(\text{Mean - Median}\right)$
Now, $\text{Mean}-\text{Mode}=\pm 63$ (Given)
$\Rightarrow \text{Mean - Median}=\frac{\pm 63}{3}=\pm 21$
$\therefore$ difference between mean and median is $21$