Percentage change over multiple years

Question

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!

Answer 1

Percentage change over all years.

$\frac{\text{Final Value - Initial Value}}{\text{Initial Value}} \times 100$

= $\frac{160 - 30}{30} \times 100$

This is correct method.

If you take account of all terms still you got 130. So its the right method i.e $+83-7-56-31+1+0+43-50+56+31-44+104 = 130$

Answer 2

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.