Question

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

 

Answer 1

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`