Hi cmbarona,

Methods 2 and 3 should give you the exact same answer, because the factor of 1/5 cancels from both the numerator and denominator of Method 2, and you just end up with the ratio from Method 3.

Neither of these is what you want. If the question you're trying to answer is "by this point in the year, what percentage of our annual earnings have we typically received?", then Method 1 provides the answer to that question. You're averaging the percentages, which gives you what fraction of the total annual earnings you've earned YTD (year-to-date), *on average*, over the last 5 years.

To illustrate why Method 2 is not what you want, it's because the average of the *absolute* YTD earnings in two different years is misleading, since YTD earnings would be very different in different years if the total donation amount were very different in those two years. I think this is best illustrated with a very simplistic example, let's say you got only $1000 in year 1, but $5000 in year two. Furthermore, let's say that by the end of June, you had $750 in year 1 and $2500 in year 2. So, to summarize:

C1 = $750

C2 = $2500

T1 = $1000

T2 = $5000

Using Method 1: P1 = 750/1000 = 0.75, and P2 = 2500/5000 = 0.5, and therefore P_avg = P1+P2/2 = (0.75+0.5)/2 = 1.25/2 = 0.625

Here we got an answer that is representative what's actually happening. By this point in year1 you had 75% of your donations, and by this point in year 2, you had 50% of your donations, so on average, you get about 62.5% of your donations by mid-year

Using Method 2: C_avg = (C1 + C2)/2 = (750 + 2500)/2 = 3250/2 = 1625

T_avg = (T1 + T2)/2 = (1000 + 5000)/2 = 6000/2 = 3000

P_avg = C_avg / T_avg = 1625/3000 = 0.54

So, despite the fact that in year 1, you got *75% of your donations by mid-year* (which is a **lot** more than half) you're reporting an average mid-year percentage earnings of only 54%. That's clearly not right. Your average percentage value is low because the *absolute* earnings in year 1 were low, illustrating that this is not the right statistic.

One final suggestion: you could considering quantifying this using more than just a single number. If you have YTD earnings for every single month of the year, for several years, you could make a plot (a graph) of the cumulative percentage earnings vs. time for each year, and compare them. Maybe in some years it increases towards 100% very steeply at first, because most donations came in early in the year and then it tapers off. Or maybe, every year, it's close to a straight line (with constant slope), because the rate of donations is steady over the year: you get about the same amount coming in every month). That graph, I think, would be very informative to look at.