What is the correct calculation here?

Question

I bought some books as below

I want to consolidate these expenses together like this

Method 1

Purchase Rate in Table2 = AVERAGE(37.44+22.97+23.02) = 27.81
Quantity in Table2 = 50
Therefore Amount total in Table2 = 27.81*50 = 1390.5
But from Table1, Amount total is only 1236.37

Method 2

Amount total from Table1 = 1236.37
Quantity in Table2 = 50
Therefore, Purchase Rate in Table2 = 1236.27/50 = 24.7274
But average Purchase Rate from Table1 = AVERAGE(37.44+22.97+23.02) = 27.81

Which method is correct here? Feels like a simple calculation, but I'm definitely missing something here.

Answer 1

Your second answer is correct. You have to consider not just the base price, but how much is being bought.

For example, say you have a lottery and you have a 1% chance of getting \$0 and a 99% chance of getting \$10. Is the average going to be \$5? Of course not; it will be almost \$10. Averages between one individual thing and another can be calculated using the simple $\frac{a+b}{2}$ formula, but when multiple instances of the same thing occur, that's when things get complicated.

This is also the basis for expected value. Take a Google search to learn more! In essence, expected value is just arithmetic means, but with much more factors in it.

-FruDe