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I'm trying to calculate the average percent change of 3 points in time that I have.

The time periods are from 2011 to 2013

I calculated the percent change for 2011 to 2012 (2012-2011)/(2011) 2012 to 2013 (2013-2012)/(2012) and 2011 to 2013 (This is the part I'm worried about)--(2013-2011)/(2011(

After getting the results I decided to average them, but I'm worried that the percent change I got for 2011 to 2013 includes (though not seen) changes that happened in the middle period of 2012.

I know that each number is a stand alone, but I was just wondering if adding the three values I get for the percent change and dividing by 3 yields data that is actually useful or if it is incorrect to do so.

user3253967
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1 Answers1

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If the increase from $2011$ to $2012$ is $a$, the value in $2012$ is $(1+a)$ times the value in $2011$. Similarly if the increase from $2012$ to $2013$ is $b$, the value in $2013$ is $(1+b)$ times that in $2012$. Then the increase from $2011$ to $2013$ is $a+b+ab$. If the increases are small, the $ab$ term is quite small. It makes some sense to average $a$ and $b$, getting approximately the growth that (if repeated twice) results in the same growth from $2011$ to $2013$. It makes no sense to average the three.

Ross Millikan
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  • Well I have the values already (it's based off a population), so for instance I had a population of 4000 in 2011, 4500 in 2012 and 3500 in 2013.SO I calculated the percent change for each point so (4500-4000)/(4000) for 2011 to 2012 and (3500-4500)/(4500) for 2012 to 2013 and then finally (3500-4000)/(4000) for 2011 and 2013. Once I got those percent values though, I wanted to get an average for the time frames. – user3253967 Feb 06 '14 at 02:54
  • The first is the average for 2011-2012, the second is the average for 2012-2013. The third has no new information, in fact less because you don't know the change each year. So you should discard it in preference for the first two. It might take some noise out to average the first two. You should think whether a geometric average makes more sense. – Ross Millikan Feb 06 '14 at 04:25