Growth rates of averages does not make sense. Why?

Been struggling with this and can’t explain it.


Link to google sheets

I need to compute the revenue per store and the implied growth rate of the revenue per store. What I can’t understand is why the overall CAGR (highlighted in green) of 5.49% can be lower than any of the components that make it up (highlighted in yellow). Shouldn’t it fall between the range of its components ie between 7.18% and 17.87%. I have triple checked it and do not find any mistakes in my computation.

Thank you.

If you look at the CAGRs per store per year, you will see that year 2024 is when the weighted average’s CAGR falls below any of the components. I’m not a quant, but it looks like you are crossing a threshold where after 2024 all the CAGRs start to fall, and the time impact of the weighted average CAGR is making it fall faster than the others.

not really understanding you here. Can you please elaborate? Thanks.

there is nothing wrong with your math, brah - your intuition is off when it comes to the average per store. It comes down to this - the total revenue is the sum of segment revenues, so of course the total revenue CAGR falls between the individual segment revenue CAGRs.

but the total revenue per store is not the sum of the individual segment revenue per store, so there is no need for it CAGR to fall between the individual segment revenue per store CAGRs. Consider this:

Year 1: 1 store @ $90 per store and 1 store @ $10 per store, total revenue $100 for 2 stores total, so total revenue per store $50

Year 2: 1 store @ $100 per store (rev per store went up by $10 in this segment), and 2 stores @ $25 per store (you opened another store in the second segment and increased revenue per store by $15). Total revenue is now $150 for 3 stores total, so total revenue per store is still $50…

Yea, this is what I meant by looking at the trends over time. While I don’t know the math reason like Mobius, I think you are just comparing two different things. If you took the sum of all your sales per stores, then you’d get a number I think you are looking for. You may even get it if you took an equally weighted average of the revenue per store. But your current calculation is the weighted average and the weights are changing through time along with the exponential impact of the calculation

Thanks both! really appreciate the help :slight_smile:

If you are 40% English and 15% French, based on the math, how does the average make you a Native American? Please discuss. Tanks.