- #1
adjacent
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Homework Statement
Obviously this is not a homework question,but I put this here as this looks like one.
Lets see.
The average of something is [itex]\frac{Sum of all the numbers}{Amount of the numbers.}[/itex]
For example,1,2,3,4,5,6
The average is 3.5 which is also the middle of the sequence.
If the numbers were 1,4,8,9,11
Average is 6.6
Which is not the middle of course.
Anyway,Why does the average give the middle number?
The Attempt at a Solution
Let x and y be integers.
[itex]\frac{x+y}{2}[/itex] =Average
But I don't see the logic behind this.
Also let x and y be integers.and y is the largest number
First y-x to find the range.
So [itex]\frac{y-x}{2}[/itex] gives the middle number between y and x range
So we add the middle number to the x to get the middle number between y and x.
Rearranging,this is same as the average formula.
So is there another way of logicing(1) this?
P.S(1) Couln't think of another word