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If the difference of mode and median of a data is 24, then find the difference of median and mean.

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#### Solution

Given that the difference of mode and median of a data is 24. That is,

MODE - MEDIAN = 24

⇒ MODE = MEDIAN + 24

We have to find the difference between median and mean

We know that

MODE = 3 × MEDIAN - 2 × MEAN

⇒ MEDIAN + 24 = 3 × MEDIAN - 2 × MEAN

⇒ 24 = 3 × MEDIAN - MEDIAN - 2 × MEAN

⇒ 24 = 2 × MEDIAN - 2 × MEAN

⇒ 2 × MEDIAN - 2 × MEAN = 24

⇒ 2( MEDIAN - MEAN ) = 24

⇒ MEDIAN -MEAN = `24/2`

⇒ MEDIAN - MEAN = 12

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