Should grand total equal average of sub total
 

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?
--
Thanks, Bonnie

Should grand total equal average of sub total
 

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

Should grand total equal average of sub total
 

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

Should grand total equal average of sub total
 

James,
Thank you so much for your response. I belive you did understand my
quesstion. If then, the grand total average and the average of subtotals are
not necessarily the same.......which average is the true answer?

A) I calculated the grand total by summing all data (10 columns of figures
and dividing by the actual number of imputs (not couonting zero's.)

B) I calculated the sub total averages by adding each column and dividing
that sum by the number of imputs for that particular column.

When I add the sub total averages from the 10 columns and divide by 10,
the average does not match the grand total computed using approach (A).

It is really important for me to know which average is the true answer.
If you can help me out I will be wxtremely grateful
Thanks, Bonnie


"James Silverton" wrote:

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

Should grand total equal average of sub total
 

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.

--
Regards

Roger Govier


"Bonnie" wrote in message
...
James,
Thank you so much for your response. I belive you did understand
my
quesstion. If then, the grand total average and the average of
subtotals are
not necessarily the same.......which average is the true answer?

A) I calculated the grand total by summing all data (10 columns of
figures
and dividing by the actual number of imputs (not couonting zero's.)

B) I calculated the sub total averages by adding each column and
dividing
that sum by the number of imputs for that particular column.

When I add the sub total averages from the 10 columns and divide
by 10,
the average does not match the grand total computed using approach
(A).

It is really important for me to know which average is the true
answer.
If you can help me out I will be wxtremely grateful
Thanks, Bonnie


"James Silverton" wrote:

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

Should grand total equal average of sub total
 

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.
--
-John Northwest11
Please rate when your question is answered to help us and others know what
is helpful.


"Bonnie" wrote:

James,
Thank you so much for your response. I belive you did understand my
quesstion. If then, the grand total average and the average of subtotals are
not necessarily the same.......which average is the true answer?

A) I calculated the grand total by summing all data (10 columns of figures
and dividing by the actual number of imputs (not couonting zero's.)

B) I calculated the sub total averages by adding each column and dividing
that sum by the number of imputs for that particular column.

When I add the sub total averages from the 10 columns and divide by 10,
the average does not match the grand total computed using approach (A).

It is really important for me to know which average is the true answer.
If you can help me out I will be wxtremely grateful
Thanks, Bonnie


"James Silverton" wrote:

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