TITLE: Simple question regarding ratio and average
QUESTION [16 upvotes]: I have 2 lists of numbers (with an equal number of numbers in each). Each number is then divided by the number of which it is paired with (by index), and a ratio is received.
I then want to calculate the global average ratio, so I try 2 ways:

Sum all numbers in each column, and divide one with the other.
Make an average of all ratios I have received from the calculation above.

Both give me different results.
How could that be? And what would be considered the true global ratio average?
Example lists:
1  : 1 = 1
2  : 1 = 2
3  : 2 = 1.5
4  : 2 = 2
-----------
         1.625 average
10 : 6 = 1.667

REPLY [2 votes]: Asking which is "the true global ratio average" brings you very close to Simpson's paradox where, for example, treatment A can be better for men than treatment B, and also better for women, but worse overall. There is an active literature on how to deal with the paradox when it arises.