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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
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B
9:10
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C
9:7
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D
8:11
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Solution

The correct option is A $$9:10$$
We have 
Mode $$:$$ Median $$= 6:5$$ 
$$ \Rightarrow $$ Mode $$= 6\lambda, $$  Median $$= 5\lambda$$
Now,
Mode $$ = 3$$ Median $$ - 2$$ Mean
$$\Rightarrow \quad 6\lambda = 3\times5\lambda - 2$$ Mean 
$$\Rightarrow$$ Mean $$= \displaystyle\frac{9}{2}\lambda$$
$$\therefore $$  Mean $$:$$ Median $$= \displaystyle\frac{9\lambda}{2}:5\lambda = 9:10$$

Mathematics

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