I have the following data:
$$\begin{array}{c|c|c}2010 & 2011 & 2012 \\\hline 50 & 20 & 30 \\\end{array}$$
How would the percent change be calculated?
Like this: $$100\times\left(\frac{|30-50|}{50}\right)\quad?$$
$\endgroup$1 Answer
$\begingroup$It depends on whether you want the absolute percent change (i.e., a decrease still produces a positive number), or the relative percent change (i.e. a decrease produces a negative number). It also depends on which times you are looking at.
So, to compute the absolute percent change from 2010 to 2012, your formula is correct, and we get $$100\times\left(\frac{|30-50|}{50}\right)=100\times\left(\frac{20}{50}\right)=40\%.$$
But to compute the relative percent change from 2010 to 2012, we drop the absolute value from the formula, and get $$100\times\left(\frac{30-50}{50}\right)=100\times\left(\frac{-20}{50}\right)=-40\%.$$
To compute the relative percent change from time $A$ to time $B$, take the data points at $A$ and $B$ (let's call them $f(A)$ and $f(B)$, respectively), and compute $$100\times\left(\frac{f(B)-f(A)}{f(A)}\right)$$ To compute the absolute percent change, you'd take the absolute value.
In this problem, I believe it is implied that the times you should be comparing are the first and the last, but a different problem might ask you about comparing different times, in which case you'll have to be careful to use the data points corresponding to those times.
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