Question

If the ratio of mode and median of a distribution is $6:5$, then the ratio of its mean and median is

• A. $8:9$
• B. $9:10$
• C. $9:7$
• D. $8:11$

Answer 1

Answer: (B)

$9:10$

We have
Mode $:$ Median $=6:5$

$\Rightarrow$ Mode $=6\lambda ,$ Median $=5\lambda$

Now,
Mode $=3$ Median $-2$ Mean
$\Rightarrow 6\lambda =3\times 5\lambda -2$ Mean

$\Rightarrow$ Mean $=\frac{9}{2}\lambda$
$\therefore$ Mean $:$ Median $=\frac{9\lambda }{2}:5\lambda =9:10$