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

Answer:

x=7

y=8

Step-by-step 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:

$median=\frac{n+1}{2}\\\\Median=3^{rd} \ term\\\\=x$

Hence:

$b=median=mean\\\\b=x\\\\\therefore mean=median=x$

-Applying the mean formula:

$\bar x=\frac{1}{n}\sum{x_i}\\\\\therefore 5x=4+6+x+y+10\\\\4x=20+y\\\\x=5+0.25y$

#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