# Percentage change over multiple years

I have data for the number of mice in an area of 13 years.

$\begin{bmatrix} \text{Year} & \text{#mice} \\ 1995 & 30 \\ 1996 & 113 \\ 1997 & 106 \\ 1998 & 50 \\ 1999 & 19 \\ 2000 & 20 \\ 2001 & 20 \\ 2002 & 63 \\ 2003 & 13 \\ 2004 & 69 \\ 2005 & 100 \\ 2006 & 56 \\ 2007 & 160 \\ \end{bmatrix}$

I want to know the net percentage change over the 13 years.

I have done $\frac{160-30}{30}\cdot 100 = 81.25\text{%}$, is this correct, is just doesn't seem right to me as it doesn't take into account all the other values. So I decided to add all the differences between each year, which = $130$, I summed the values, which = $819$. So I tried $\frac{130}{819} \cdot 100 = 15.87\text{%}$, which seems more reasonable, but is it mathematically correct?

Thanks in advance for any help!

• Depends on what do you mean by "over the 13 years". As it stands, you need to take into account only the first year and the last year (which is exactly what you did). – barak manos Jan 4 '17 at 14:49

$\frac{\text{Final Value - Initial Value}}{\text{Initial Value}} \times 100$
= $\frac{160 - 30}{30} \times 100$
If you take account of all terms still you got 130. So its the right method i.e $+83-7-56-31+1+0+43-50+56+31-44+104 = 130$
If you want to say what the percentage increase is from $1995$ to $2007$, it is $\frac {160-30}{30}\approx 433\%$. It appears you divided by $160$ when you did the calculation. The sentence doesn't mention the population in the intervening years, so why should it matter? Adding up the numbers for the years might give you a figure for the total number of mice that had lived there, but only if each mouse lives a year. If you want to reflect the intervening years, you can compute the average and variance of the number of mice.