I understand what the problem is asking and I understand how they got the solution, but I'm confused as to why the solution is correct.
The problem is asking for the average value of two average values, so why divide again by all 12 packages when the individual average values were already divided by 8 and 4 respectively? It seems like we are summing up the values and then dividing by 12 twice.
I even tried making up a simplified example to see what would happen if all the individual values were known:
Average of 1, 2, 3, 4 = (1 + 2+ 3 + 4)/4 = 5/2.
Average of 1,2 = (1 + 2)/2 = 3/2.
Average of all of the above values = (1 + 2 + 3 + 4 + 1 + 2)/6 = 13/6
But if I were to use the OG solution on this simplified example, it would be
(5/2) + (3/2) / 6 = (8/2)/6 = 8/12 = 2/3
2/3 is not equal to 13/6.
I'm missing some logic that the book just isn't detailing. I really want to understand this problem. Can anyone help?
The problem is asking for the average value of two average values, so why divide again by all 12 packages when the individual average values were already divided by 8 and 4 respectively? It seems like we are summing up the values and then dividing by 12 twice.
I even tried making up a simplified example to see what would happen if all the individual values were known:
Average of 1, 2, 3, 4 = (1 + 2+ 3 + 4)/4 = 5/2.
Average of 1,2 = (1 + 2)/2 = 3/2.
Average of all of the above values = (1 + 2 + 3 + 4 + 1 + 2)/6 = 13/6
But if I were to use the OG solution on this simplified example, it would be
(5/2) + (3/2) / 6 = (8/2)/6 = 8/12 = 2/3
2/3 is not equal to 13/6.
I'm missing some logic that the book just isn't detailing. I really want to understand this problem. Can anyone help?
