Today, my case partner asked me to estimate the number of weddings per year in a given country. Let's arrive to the core of the case in simplified terms. After dividing the population in four age sections, we came up with this situation:

0-20: 0 weddings

21-40: 200 weddings

41-60: 100 weddings

61-80: 20 weddings

Now, in this given population we have 320 potential weddings. I was going to divide 320 weddings by 60 years, but my case partner stopped me and told me that I had to divide by 20 years (200/20 + 100/20 + 20/20 or 320/20).

The two approach are not equivalent, hence one is wrong. Which one and why?

PS: If dividing by 20 years is correct, I have another doubt. Let's say that we approach the case differently and we segment the population in only one big age cluster (21-80). Now, in order to have the same number of weddings per year (320/20 = 16), the number of potential wedding in the same population should be 16*60 = 960. For this reason, I suspect that dividing by 20 is not the correct option.

Many thanks for the effort!

(edited)

Hi Henning! Thank you for the explanation. That's true, your approach is much simpler. However, isn't an overestimation not to exclude people belonging to the 0-18 age group? I would have used a shorter time frame than life expectancy (e.g. 60 years, approx. the 18-80 range), is that an error? Anyway, the approach I described above was incomplete. I did not start the case by estimating the number of weddings per age bracket. My starting assumption was that only a fraction of the population actually get married in their lifetime and most of them get married when they are in the 21-40 age bracket. So, I divided into age groups to estimate how many people marry in their lifetime within a given population. I divided the total number of people that marry by 2, to calculate the number of weddings. Finally, I divided the total number of weddings by 60 years, assuming that are equally distributed over time.

Interesting point - thanks for calling me out on this! My approach implicitly assumes that the population is stable. The not-yet in marrying age population only matters if there was a recent increase in birth rate (in the last 18 years). If birth rate is not constant, you should indeed take the birth rate as of [average age at wedding] years ago. I'd still go without the age brackets. This is a good approach when the age actually drives something like consumption behavior. But since the age doesn't matter for the overall consumption here, I'd leave it out to make the case simpler.

Thank you very much for the explanation, really clear!