Hi everyone,

I have a math question I'm hoping someone here can help me with. I think that I understand vaguely the basic principle involved, but my clarity could stand to be improved and I'm willing to bet that someone here is clever enough to explain it.

Let's say that I want to calculate an average percentage per month over a four month period. Say it's the percentage of people in a room at the stroke of noon on the first day of the month who have red hair, or whatever.

Month 1: 1 person, 1 redhead (100%)
Month 2: 2 people, 1 redhead (50%)
Month 3: 3 people, 1 redhead (33%)
Month 4: 4 people, 1 redhead (25%)

There are two ways I can see to approach this problem. The obvious way is to add the percentages and divide by four, resulting in an average of 52% per month.

However, a second way of approaching it produces a different answer and I'm hazy about why.

The second method is to average the two numbers separately. The average number of people in the room per month is 2.5 (1+2+3+4 / 4), and the average number of redheads in the room per month is 1 (1+1+1+1 / 4).

But by that method, the average percentage of redheads in the room is 40% (1/2.5). This is different from the previous answer. Obviously only one can be correct. My gut instinct is that the second method produces a more accurate result, since the first method adds the percentages together without regard to the fact that the denominators are different each month.

If you do make the denominators the same (12/12, 6/12, 4/12, 3/12), then each method produces an identical answer. But while making equivalent fractions might work for pure math, we're talking about people, and 12 redheads in a room of 12 people is fundamentally different from 1 redhead in a room of 1 person.

Is my thinking correct? Is 40% the correct answer? Does any of this make sense?

My thanks in advance for any help.