Question

5 whole numbers are written in order, 4, 6, x, y, 10. The mean and median of the 5 numbers are the same so what are the values of x and y

Answer 1

Answer: The value of x is 7 and the value of y is 8.

Step-by-step explanation:

It is given that 5 whole numbers are written in order, 4, 6, x, y, 10. The mean and median of the 5 numbers are the same.

`Mean=\frac{\text{Sum of observations}}{\text{No. of observations}}`

`Mean=(4+6+x+y+10)/(5)`

`Mean=(20+x+y)/(5)`

The 5 numbers are arranged in ascending order. The total numbers are 5 which is odd number so the median is
`((n+1)/(2))_(th)` term.

n=5

`(n+1)/(2)th=(5+1)/(2)th=3rd`

The third term is median. So the median is x.

Since mean and median are same.

`(20+x+y)/(5)=x`

`20+x+y=5x`

`20=4x-y` ... (1)

Since the whole numbers are arranged in the ascending order therefore the value of x and y must a whole number greater than 6 and less than 10.

Put x=7 in equation (1).

`20=4(7)-y`

`y=8`

Therefore, the value of x and y are 7 and 8 respectively.

Put x=8.

`20=4(8)-y`

`y=12>10`

Therefore the value of x can not be 8 or not more than that.