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Question
If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean
Solution
Given that the ratio of mean and median of a certain data is 2:3. That is,
MEAN : MEDIAN = 2:3
`⇒(MEAN)/(MEDIAN)=2/3`
`⇒3xx MEAN = 2 xx MEDIAN`
`⇒MEDIAN = 3/2 MEAN`
We know that
` MODE = 3 xx MEDIAN - 2 xx MEAN `
`⇒MODE = 3 xx 3/2 MEAN -2 xx MEAN `
`⇒MODE = (9/2-2) MEAN`
`⇒(MODE)/(MEAN) = 9/2 -2`
`⇒ (MODE)/(MEAN)=5/2`
`⇒ MODE : MEAN = 5:2`
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Is it the correct answer and why?
