Question

If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median. 

Answer 1

Given that the ratio of mode and median of a certain data is 6:5. That is,

MODE : MEDIAN = 6.5

`⇒ (MODE )/(MEDIAN )= 6/5`

`⇒ 5 xx MODE = 6 xx MEDIAN`

`⇒MODE = 6/5 MEDIAN`

We know that

`MODE xx 3 xx MEDIAN -2 xx  MEAN`

`⇒6/5 MEDIAN = 3 xx MEDIAN - 2 xx MEAN`

` ⇒ 2 xx MEAN = (3-6/5) MEAN `

`⇒ 2 xx MEAN = 9/5 MEDIAN`

`⇒ 2  MEAN = 9/10 MEDIAN`

`⇒ (MEAN)/(MEDIAN) = 9/10`

`⇒ MEAN : MEDIAN = 9:10`