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