Difference of the averages of two ranges

[Tommy]

Can someone explain mathematically why the difference of the sum of the
average of row two and three (Range D23) as shown in cell E3 is different
than the average of each individual difference in range A4:C4 as shown in
cell E4.
It is not obvious to me.

test 1 test 2 test 3 Average Diff
10 5 10 8,33
6 1 2 3 -64,00 %
-40,00 % -80,00 % -80,00 % -66,67 %

 

[Reeza]

Can someone explain mathematically why the difference of the sum of the
average of row two and three (Range D23) as shown in cell E3 is different
than the average of each individual difference in range A4:C4 as shown in
cell E4.
It is not obvious to me.

test 1  test 2  test 3  Average Diff
10      5       10      8,33    
6       1       2       3       -64,00 %
-40,00 %        -80,00 %        -80,00 %                -66,67 %

Weighted Average vs Average
Test 2 is 5 not 10 like the others, but in percentage points they
all become the same scale or same weights. Change Test 2 to 10 and 2
and you should get the same numbers or calculate a weighted average
rather than average...depends on what you're looking for at the end of
the day.

HTH,
Reeza