Average Growth Rate for Year 1 across 5 groups

Question

Lets suppose that I am measuring the total number of online visitors to 5 websites on a monthly basis. I have this data for the months of Jan - Dec.

What I want to understand is "What is average yearly growth rate for the websites?"

That is, imagine I am doing something to these websites and I want to say to someone that these the 5 websites, which are representative of some population, on average will give a website a x% yearly growth rate in visitors in the first year.

Since I have measured this for 12 months for each website, finding the growth rate in visitors for one website would be the standard (t(month12) - t(month 1))/t(month 1). If wanted to find the yearly average growth rate across all 5 websites, what would I do? Would it be safe to average the yearly growth rates? I am not looking for an extremely formal method for this. I just wanted to know if there are in dire dangers in doing this when trying to get a genereal reflection of the yearly growth rate across the 5 website. Hopefully that makes sense. Thanks!

Answer 1

Let say you have 2 websites with $m_1$ and $n_1$ visitors an the beginning of the year. And $m_2$ and $n_2$ visitors at the end of the year. The average (yearly) growth rate then is $\frac{m_1}{m_1+n_1}\cdot \frac{m_2-m_1}{m_1}+\frac{n_1}{m_1+n_1}\cdot \frac{n_2-n_1}{n_1}$

This term can be simplified to $\frac{1}{m_1+n_1}\cdot (m_2+n_2-m_1-n_1)$

I hope you can generalize it to the case of n websites.

Remark: If you want to calculate the average yearly growth rate of one website, you have to calculate $\frac{V_{y,m} - V_{y-1,m}}{V_{y-1,m}}$.

Thus you need the Information about the visitors of the $m^{th}$ month of the previous year ($V_{y-1,m}$). In you case $V_{y-1,12}$

Answer 2

First you have to define what you mean by yearly growth on one website based on the data you have. Probably the best approach is to do an exponential fit to the monthly data, getting a growth rate per month, $r$. Then the yearly growth is $(1+r)^{12}-1$ Then if you want to average the yearly growth rates across the sites, you can do that-just add them up and divide by $5$. Whether that is meaningful is left as an exercise.