Simple question regarding ratio and average

How could that be?

It is more instructive to regard just the case of lists of length 2:

You want to have

$$\frac{a}{c}+\frac{b}{d} = \frac{a+b}{c+d}.$$

But this is almost never true, there is a reason for the more complicated way to add fractions.

With 27 numbers, it does not get better.

Edit:

what would be considered the true global ratio average?

It depends on your situation what you want to calculate. For example, let's say you know of every person in a country: how much they earn and how much they spend on food.

1. Sum all numbers in each column, and divide one with the other.

• This gives you the ratio of the averages, which tells you what percentage of the total income in the country is spent on food.

• Outliers (in this case, the few very rich people who spend a relatively high amount on food) significantly influence the ratio of the averages.

• Use this if you want to know how food price rises impact the part of the economy that produces and sells food

2. Make an average of all ratios from the calculation above.

• This gives you the average of the ratios, which tells you the average percentage people spend on food.

• Outliers have less of an effect.

• Use this if you want to know how food price rises impact people

The answer to your first question is the observation that $\frac{a}{b} + \frac{c}{d}$ is in general not equal to $\frac{a+c}{b+d}$. In other words, the average of ratios is not necessarily equal to the ratio of sums.

As regards the true global ratio average is concerned- I think the answer is context specific. A meaningful answer can only be given if you could shed some light on the nature of the numbers you have.