If the difference between mode and median of a data is 18, Find the difference between mean and median.

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Solution

The correct option is A 9
Mode - Median = 18 (Given) ....(i)
Mode = 3 Median - 2 Mean .....(ii)
Eliminating mode from $(i)$ and $(i i)$ , we get
$\Rightarrow$ 18 + Median = 3 Median - 2 Mean
$\Rightarrow$ 18 = 2 Median - 2 Mean
$\Rightarrow$ Median - Mean = 9
Difference between Mean and Median is 9.

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M o d e = 3 M e d i a n - 2 M e a n

Find difference between mean and median. If the difference between mode and median of a data is 18, use the relation
Mode = 3 Median - 2 Mean.

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