Question

The mode of a data exceeds its mean by $12$. By how much does its mode exceed the median?

• A. $8$
• B. $12$
• C. $0$
• D. $10$

Answer 1

The correct option is A $8$

We know that,

3 median=Mode +2Mean

Let Median $=M$

mode $=m$

Mean $=\overline{x}$

Since, $m=\overline{x}+12$

$3M=m+2\overline{x}$

$3M=\overline{x}+12+2\overline{x}=3\overline{x}+12$

$M=\overline{x}+4$

$M=m-12+4$

$M+8=m$

So, mode exceeds median by $8$.