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If the ratio of mean and median of a certain data is 2:3, then what is the ratio of its mode and median ?

Using the empirical relation \(\text{Mode} = 3\text{ Median} - 2\text{ Mean}\), let \(\text{Mean} = 2k\) and \(\text{Median} = 3k\). Then \(\text{Mode} = 3(3k) - 2(2k) =…

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If the ratio of mean and median of a certain data is 2:3, then what is the ratio of its mode and median ?

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Using the empirical relation Mode=3 Median−2 Mean\text{Mode} = 3\text{ Median} - 2\text{ Mean}, let Mean=2k\text{Mean} = 2k and Median=3k\text{Median} = 3k. Then Mode=3(3k)−2(2k)=5k\text{Mode} = 3(3k) - 2(2k) = 5k, so the ratio of mode to median is 5k:3k=5:35k : 3k = 5:3.

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