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:

We have

$Mode: Median = 6 : 5 \Rightarrow Mode = 6 λ, Median = 5 λ$

Now,

$\begin{array}{l} Mode = 3 Median - 2 Mean \\ \Rightarrow 6 λ = 3 \times 5 λ - 2 Mean \Rightarrow Mean = \frac{9}{2} λ \\ ∴ Mean : Median = \frac{9 λ}{2} : 5 λ = 9 : 10 \end{array}$

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