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

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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