Why is Percent Change Calculated Like This?

[AAAA]

Homework Statement

The formula for price elasticity in my micro/macroeconomics course is:
elasticity =

For those unable to view the image:
(change in quantity / avg quantity)/(change in price / avg price)

My question is: Why is it that the average quantity/price is used instead of just the initial quantity/price (in reference to the part in brackets in the numerator and denominator?

In economics, the value which the equations spits out has significance:
>1 = elastic
1 = unit-elastic
<1 = inelastic

The Attempt at a Solution

I thought you would just divide by initial quantity; like how you would in a rate of change formula:
change x/change y
so [(q2-q1)/q1]/[(p2-p1)/p1]

I tried the 2 formulas on an excel spreadsheet, with the following results:
Original equation on right, my equation on the right
http://puu.sh/l4RCy/efce1c651b.png
NOTE: The value that looks to be 1 is really 0.96, with less decimals

 

[mfb]

That expression gives the same result in both directions, so the coefficient depends on the two states only, not on the arbitrary choice which one is the "initial" state (it is not a time series).

 

[AAAA]

That expression gives the same result in both directions, so the coefficient depends on the two states only, not on the arbitrary choice which one is the "initial" state (it is not a time series).

Oh, alright, cool. It makes sense because the formula is only concerned with magnitude, and not direction.

Thanks!