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I am currently coding a script which displays data for a company intranet. I am stuck with a question that seemed pretty simple, but turned out to give me headaches.

We have the following scenario:

  • Store A has 70 male customers and 100 female customers - (170 total)
  • Store B has 50 male customers and 230 female customers - (280 total)

Now, I learned that in order to display the average male/female ratio I have to calculate:

$$\frac{\text{Male Store A} + \text{Male Store B}}{170 + 280} = X $$

$X * 100 = 28.9\%$ for males, $71.1\%$ for females

Yet when thinking it over, it doesn't show the real average, because the total number of clients isn't the same (170 vs 280).

So I did a second approach, which is first separating the percentage by store, and then calculating the average percentage:

  • Males, Store A: $\cfrac{70}{170} * 100 = 41.2\%$
  • Males, Store B: $\cfrac{50}{280} * 100 = 17.9\%$

And then divide it:

$$\frac{41.2\% + 17.9\%}{2} = 29.6\% $$

So in the second case, rounded up, male ratio is 29.6% instead of 27.3%

Then I showed both calculations to somebody who is better in math then me, and he told me that both are wrong. He said I should use "weighted average", but when I do i get exactly the same average percentage like in the first calculation.

What am I doing wrong?

Background: We have a lot of stores, each with a different number of female and male clients. I want to have a percentage of the average client gender, but taking into account the different amount of the guests in each store.

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Okay, so I decided to stick to the weighted average method. Here is a good calculator to cross check your results:

http://www.handymath.com/cgi-bin/average.cgi

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