Excel averaging VS dividing

[Mark]

I am working on a spreadsheet. My ficticous numbers from
cells A1, B1, C1 are 500, 700, and 600. The numbers in
cells A2, B2, C2 are 2, 6, and 11. If you divide the three
numbers in row 2 by the three in row 1 you get 0.004(A3),
0.008571(B3), and 0.01833(C3).

If you sum row 1 you get 1800(D1), sum row 2 you get 19
(D2). If you divide cell D2 by D1 you get 0.010556(D3).

Now for the part I don't understand...If you sum cells A3,
B3, and C3 and divide by 3 shouldn't you get the same
answer as when we divided D2 by D1? If not, WHY. (I got
0.010302)

 

[jr]

what you're implying is that:
(A2/A1 + B2/B1 + C2/C1) / 3 = (A2 + B2 + C2) / (A1 + B1 +
C1)
Which is clearly not true.

 

[Steve McBride]

Addition and multiplication are commutative processes, while subtraction and
division are not.

Commutative: Mathematics not dependent on order: Giving the same result in
mathematics or logic irrespective of the order in which two or more terms or
quantities are placed.

HTH!
Steve