Question

If the average (arithmetic mean) of the five numbers x, 7, 2, 16, and 11 is equal to the median of the five numbers, what is the value of x?1) 7 < x < 11

2) x is the median of the five numbers

Answer 1

`x=9`

Explanation:

We have been given that the average (arithmetic mean) of the five numbers x, 7, 2, 16, and 11 is equal to the median of the five numbers. We are asked to find the value of x.

Since we have been given that
`7<x<11`, so we can arrange our given data in ascending order as:

2, 7, x, 11, 16.

We are also told that x is the median of 5 numbers, so we can set an equation as:

Average of 5 numbers = Median

`(2+7+x+11+16)/(5)=x`

`(x+36)/(5)=x`

Let us solve for x.

`(x+36)/(5)*5=5*x`

`x+36=5x`

`5x=x+36`

`5x-x=x-x+36`

`4x=36`

`(4x)/(4)=(36)/(4)`

`x=9`

Therefore, the value of x is 9.