Question

Question POOLE

Homework Progress
729
Five whole numbers are written in order
4 6 x y
10
The mean and median of the five numbers are the same.
Work out the values of x and y.

Answer 1

`x = 7` and
`y = 8`

Explanation:

Given

4 6 x y 10

Median = Mean

Required

Find x and y

The mean is calculated as:

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

Collect Like Terms

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

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

The median which is the mid-data is x

i.e.

`Median = x`

Median = Mean; so, we have:

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

Multiply through by 5

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

`5 x=20+ x + y`

Collect Like Terms

`5 x - x=20+ y`

`4x=20+ y`

Since the numbers are in order, the values of x and y could be any of 7, 8 and 9

Such that:

`x < y`

So, we need to test the equation with these values

Let x = 7

So, we have:

`4x=20+ y`

`4 * 7 = 20 + y`

`28 = 20 + y`

`28 - 20 = y`

`8 = y`

`y = 8`

This is true for the equation.

Hence:

`x = 7` and
`y = 8`