Question

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 values of x and y.

Answer 1

x=7

y=8

Explanation:

-Given that the mean and median is the same.

-Let b=mean =median

#Given that the set is arranged in order and is even:

`median=(n+1)/(2)\\\\Median=3^(rd) \ term\\\\=x`

Hence:

`b=median=mean\\\\b=x\\\\\therefore mean=median=x`

-Applying the mean formula:

`\bar x=(1)/(n)\sum{x_i}\\\\\therefore 5x=4+6+x+y+10\\\\4x=20+y\\\\x=5+0.25y`

#Since the number are in order:

`6<x<y<10\\\\\#let\ x=7,y=8\\\#Substitute\\\\7=5+0.25(8)\\7=7\\\\`

Hence, x=7 and y=8