Should grand total equal average of sub total

B

Bonnie

My grand total average of all data is not the same as computing the average
of all sub totals. I don't understand why but it seems that the scores
should be the same. Can anyone help me?
 
J

James Silverton

Hello, Bonnie!
You wrote on Sat, 20 Jan 2007 11:30:00 -0800:

B> My grand total average of all data is not the same as
B> computing the average of all sub totals. I don't understand
B> why but it seems that the scores should be the same. Can
B> anyone help me? --
B> Thanks, Bonnie

I'm not quite sure if I understand the question but the average
of a set of averages is not necessarily equal to an overall
average.

James Silverton
Potomac, Maryland

E-mail, with obvious alterations:
not.jim.silverton.at.comcast.not
 
J

James Silverton

Hello, James!
You wrote to Bonnie on Sat, 20 Jan 2007 15:04:34 -0500:

B>> My grand total average of all data is not the same as
B>> computing the average of all sub totals. I don't
B>> understand why but it seems that the scores should be the
B>> same. Can anyone help me? -- Thanks, Bonnie

JS> I'm not quite sure if I understand the question but the
JS> average of a set of averages is not necessarily equal to an
JS> overall average.

I should expand slightly. If the groups do not overlap and the
number of values in each group is the same, the overall average
would be equal to the average of the group averages.

James Silverton
Potomac, Maryland

E-mail, with obvious alterations:
not.jim.silverton.at.comcast.not
 
R

Roger Govier

Hi Bonnie
If all groups were of equal size then there would be no difference.
Consider the following simple case

50 items totalling 200 Average =4
20 items totalling 100 Average =5

Average of "averages" =(4+5)/2 = 4.5

True Average = (200+100)/70 =4.29

In other words, the Averages need to be weighted according to their size
to give a true average as opposed to an arithmetic mean of the averages
obtained.
 
J

John Bundy

I think not including the zeroes is where your getting tripped up, create a
column with the following
100
100
50
0
100
100

the average calculated with the average() function is 75 whereas if you sum
first (450)a and divide by non-zeroes, you get 90. Excel calculates zeroes as
valid answers and it seems you do not.
 
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