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kjal

Complex Averages
 
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers spread
over 40 rows, I would need to average the last 5 which could each have a few
spaces between them. There will be no 0's or negatives in the data.

Thanks

T. Valko

Complex Averages
 
What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have a
few
spaces between them. There will be no 0's or negatives in the data.

Thanks




kjal

Complex Averages
 
Hey there. If there are only 5 numbers at some point, the 5 and 10 would be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there will
be somewhere around 30 numbers out of 40 potential leaving 10 random spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.

Thanks

"T. Valko" wrote:

What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have a
few
spaces between them. There will be no 0's or negatives in the data.

Thanks





Pete_UK

Complex Averages
 
But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?

Pete

On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10 would be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there will
be somewhere around 30 numbers out of 40 potential leaving 10 random spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.

Thanks



"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?


--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have a
few
spaces between them. There will be no 0's or negatives in the data.


Thanks- Hide quoted text -


- Show quoted text -




T. Valko

Complex Averages
 
Hmmm...

Well, let's start with this and go from there.

This will average the last 5 numbers in the range A1:J1.

Array entered** :

=AVERAGE(J1:INDEX(A1:J1,LARGE(IF(ISNUMBER(A1:J1),C OLUMN(A1:J1)-MIN(COLUMN(A1:J1))+1),5)))

If there are less than 5 numbers the formula will return a #NUM! error.

** array formulas need to be entered using the key combination of
CTRL,SHIFT,ENTER (not just ENTER)

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hey there. If there are only 5 numbers at some point, the 5 and 10 would
be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there
will
be somewhere around 30 numbers out of 40 potential leaving 10 random
spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.

Thanks

"T. Valko" wrote:

What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last
10
numbers in a row of up to 40 numbers. There will be various random
spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have
a
few
spaces between them. There will be no 0's or negatives in the data.

Thanks







kjal

Complex Averages
 
Maybe I am not explaining well or maybe it is not possible to average the
last 5 or whatever numbers of a list of numbers that has spaces but no zeros.
The range in the avg formula will be c2:c42, and the numbers will ultimatley
fill 3/4 of the fields with random spaces for the balance, So the formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces. So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.

"Pete_UK" wrote:

But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?

Pete

On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10 would be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there will
be somewhere around 30 numbers out of 40 potential leaving 10 random spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.

Thanks



"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?


--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have a
few
spaces between them. There will be no 0's or negatives in the data.


Thanks- Hide quoted text -


- Show quoted text -





T. Valko

Complex Averages
 
Try this array formula** :

=AVERAGE(C42:INDEX(C2:C42,LARGE(IF(ISNUMBER(C2:C42 ),ROW(C2:C42)-MIN(ROW(C2:C42))+1),5)))

If there are less than 5 numbers the formula will return a #NUM! error.

** array formulas need to be entered using the key combination of
CTRL,SHIFT,ENTER (not just ENTER)

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Maybe I am not explaining well or maybe it is not possible to average the
last 5 or whatever numbers of a list of numbers that has spaces but no
zeros.
The range in the avg formula will be c2:c42, and the numbers will
ultimatley
fill 3/4 of the fields with random spaces for the balance, So the formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces. So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.

"Pete_UK" wrote:

But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?

Pete

On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10
would be
the same. I hope that helps. Basically, over the course of 3 or so
months,
these numbers will begin to be added to the rows and by the end, there
will
be somewhere around 30 numbers out of 40 potential leaving 10 random
spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.

Thanks



"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP

"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and
last 10
numbers in a row of up to 40 numbers. There will be various random
spaces
between the entered numbers. So for example, if there are 15
numbers
spread
over 40 rows, I would need to average the last 5 which could each
have a
few
spaces between them. There will be no 0's or negatives in the data.

Thanks- Hide quoted text -

- Show quoted text -







Pete_UK

Complex Averages
 
So, I can now see that you are talking about a column of data - in
your first post you said the numbers were in a row !!

When you talk about "spaces" do you really mean just empty cells, or
will there be a <space in those cells? Some people use a <space to
"delete" an entry.

Pete

On Sep 25, 10:02 pm, kjal wrote:
Maybe I am not explaining well or maybe it is not possible to average the
last 5 or whatever numbers of a list of numbers that has spaces but no zeros.
The range in the avg formula will be c2:c42, and the numbers will ultimatley
fill 3/4 of the fields with random spaces for the balance, So the formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces. So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.



"Pete_UK" wrote:
But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?


Pete


On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10 would be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there will
be somewhere around 30 numbers out of 40 potential leaving 10 random spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.


Thanks


"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?


--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have a
few
spaces between them. There will be no 0's or negatives in the data.


Thanks- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -




Pete_UK

Complex Averages
 
Sorry, I thought Biff had given up, but I can now see that he's back
on the scent so I'll duck out here.

Pete

On Sep 25, 10:24 pm, Pete_UK wrote:
So, I can now see that you are talking about a column of data - in
your first post you said the numbers were in a row !!

When you talk about "spaces" do you really mean just empty cells, or
will there be a <space in those cells? Some people use a <space to
"delete" an entry.

Pete

On Sep 25, 10:02 pm, kjal wrote:



Maybe I am not explaining well or maybe it is not possible to average the
last 5 or whatever numbers of a list of numbers that has spaces but no zeros.
The range in the avg formula will be c2:c42, and the numbers will ultimatley
fill 3/4 of the fields with random spaces for the balance, So the formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces. So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.


"Pete_UK" wrote:
But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?


Pete


On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10 would be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there will
be somewhere around 30 numbers out of 40 potential leaving 10 random spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.


Thanks


"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?


--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have a
few
spaces between them. There will be no 0's or negatives in the data.


Thanks- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -




kjal

Complex Averages
 
Would it matter if it was a row or a column? I don't think it would. I was
tying to help Biff visualize what I was talking about, and I think columns
are better for that. The cells without numbers will be empty, not touched, no
data, no text. Thanks for trying.

KJ

"Pete_UK" wrote:

So, I can now see that you are talking about a column of data - in
your first post you said the numbers were in a row !!

When you talk about "spaces" do you really mean just empty cells, or
will there be a <space in those cells? Some people use a <space to
"delete" an entry.

Pete

On Sep 25, 10:02 pm, kjal wrote:
Maybe I am not explaining well or maybe it is not possible to average the
last 5 or whatever numbers of a list of numbers that has spaces but no zeros.
The range in the avg formula will be c2:c42, and the numbers will ultimatley
fill 3/4 of the fields with random spaces for the balance, So the formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces. So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.



"Pete_UK" wrote:
But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?


Pete


On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10 would be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there will
be somewhere around 30 numbers out of 40 potential leaving 10 random spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.


Thanks


"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?


--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last 10
numbers in a row of up to 40 numbers. There will be various random spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have a
few
spaces between them. There will be no 0's or negatives in the data.


Thanks- Hide quoted text -


- Show quoted text -- Hide quoted text -


- Show quoted text -





Peo Sjoblom

Complex Averages
 
It would matter


--


Regards,


Peo Sjoblom




"kjal" wrote in message
...
Would it matter if it was a row or a column? I don't think it would. I was
tying to help Biff visualize what I was talking about, and I think columns
are better for that. The cells without numbers will be empty, not touched,
no
data, no text. Thanks for trying.

KJ

"Pete_UK" wrote:

So, I can now see that you are talking about a column of data - in
your first post you said the numbers were in a row !!

When you talk about "spaces" do you really mean just empty cells, or
will there be a <space in those cells? Some people use a <space to
"delete" an entry.

Pete

On Sep 25, 10:02 pm, kjal wrote:
Maybe I am not explaining well or maybe it is not possible to average
the
last 5 or whatever numbers of a list of numbers that has spaces but no
zeros.
The range in the avg formula will be c2:c42, and the numbers will
ultimatley
fill 3/4 of the fields with random spaces for the balance, So the
formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces.
So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.



"Pete_UK" wrote:
But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?

Pete

On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10
would be
the same. I hope that helps. Basically, over the course of 3 or so
months,
these numbers will begin to be added to the rows and by the end,
there will
be somewhere around 30 numbers out of 40 potential leaving 10
random spaces
in each column assuming 40 max. So the last 5 and last 10 averages
will
develop and deviate as more data is entered.

Thanks

"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP

"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5
and last 10
numbers in a row of up to 40 numbers. There will be various
random spaces
between the entered numbers. So for example, if there are 15
numbers
spread
over 40 rows, I would need to average the last 5 which could
each have a
few
spaces between them. There will be no 0's or negatives in the
data.

Thanks- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -







T. Valko

Complex Averages
 
Would it matter if it was a row or a column?

Yes.

I've now posted examples for both!

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Would it matter if it was a row or a column? I don't think it would. I was
tying to help Biff visualize what I was talking about, and I think columns
are better for that. The cells without numbers will be empty, not touched,
no
data, no text. Thanks for trying.

KJ

"Pete_UK" wrote:

So, I can now see that you are talking about a column of data - in
your first post you said the numbers were in a row !!

When you talk about "spaces" do you really mean just empty cells, or
will there be a <space in those cells? Some people use a <space to
"delete" an entry.

Pete

On Sep 25, 10:02 pm, kjal wrote:
Maybe I am not explaining well or maybe it is not possible to average
the
last 5 or whatever numbers of a list of numbers that has spaces but no
zeros.
The range in the avg formula will be c2:c42, and the numbers will
ultimatley
fill 3/4 of the fields with random spaces for the balance, So the
formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces.
So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.



"Pete_UK" wrote:
But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?

Pete

On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10
would be
the same. I hope that helps. Basically, over the course of 3 or so
months,
these numbers will begin to be added to the rows and by the end,
there will
be somewhere around 30 numbers out of 40 potential leaving 10
random spaces
in each column assuming 40 max. So the last 5 and last 10 averages
will
develop and deviate as more data is entered.

Thanks

"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP

"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5
and last 10
numbers in a row of up to 40 numbers. There will be various
random spaces
between the entered numbers. So for example, if there are 15
numbers
spread
over 40 rows, I would need to average the last 5 which could
each have a
few
spaces between them. There will be no 0's or negatives in the
data.

Thanks- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -







RagDyeR

Complex Averages
 
FWIW,
This *array* formula will average the last 5 numbers in the range C2 to C42,
And if there are *less* then 5 numbers, it will average *any* that are
the

=AVERAGE(C42:INDEX(C2:C42,LARGE(ROW(1:41)*(C2:C42< ""),5)))

--
Array formulas must be entered with CSE, <Ctrl <Shift <Enter, instead of
the regular <Enter, which will *automatically* enclose the formula in curly
brackets, which *cannot* be done manually. Also, you must use CSE when
revising the formula.

--
HTH,

RD

---------------------------------------------------------------------------
Please keep all correspondence within the NewsGroup, so all may benefit !
---------------------------------------------------------------------------
"kjal" wrote in message
...
Would it matter if it was a row or a column? I don't think it would. I was
tying to help Biff visualize what I was talking about, and I think columns
are better for that. The cells without numbers will be empty, not touched,
no
data, no text. Thanks for trying.

KJ

"Pete_UK" wrote:

So, I can now see that you are talking about a column of data - in
your first post you said the numbers were in a row !!

When you talk about "spaces" do you really mean just empty cells, or
will there be a <space in those cells? Some people use a <space to
"delete" an entry.

Pete

On Sep 25, 10:02 pm, kjal wrote:
Maybe I am not explaining well or maybe it is not possible to average
the
last 5 or whatever numbers of a list of numbers that has spaces but no
zeros.
The range in the avg formula will be c2:c42, and the numbers will
ultimatley
fill 3/4 of the fields with random spaces for the balance, So the
formula,
hopefully, will avg the last 5 NUMBERS in the row, ignoring the spaces.
So
the numbers in the avg of the last 5 may be spread over 7 or 8 spaces.



"Pete_UK" wrote:
But if you are putting numbers into random cells in the range, how
would you know which were the last 5 or last 10 entered? Do you not
mean last by date of entry, but rather last in the sequence of data?

Pete

On Sep 25, 9:32 pm, kjal wrote:
Hey there. If there are only 5 numbers at some point, the 5 and 10
would be
the same. I hope that helps. Basically, over the course of 3 or so
months,
these numbers will begin to be added to the rows and by the end,
there will
be somewhere around 30 numbers out of 40 potential leaving 10
random spaces
in each column assuming 40 max. So the last 5 and last 10 averages
will
develop and deviate as more data is entered.

Thanks

"T. Valko" wrote:
What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP

"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5
and last 10
numbers in a row of up to 40 numbers. There will be various
random spaces
between the entered numbers. So for example, if there are 15
numbers
spread
over 40 rows, I would need to average the last 5 which could
each have a
few
spaces between them. There will be no 0's or negatives in the
data.

Thanks- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -







kjal

Complex Averages
 
Thanks Biff, that worked great. I appreciate your time on this.

KJ

"T. Valko" wrote:

Hmmm...

Well, let's start with this and go from there.

This will average the last 5 numbers in the range A1:J1.

Array entered** :

=AVERAGE(J1:INDEX(A1:J1,LARGE(IF(ISNUMBER(A1:J1),C OLUMN(A1:J1)-MIN(COLUMN(A1:J1))+1),5)))

If there are less than 5 numbers the formula will return a #NUM! error.

** array formulas need to be entered using the key combination of
CTRL,SHIFT,ENTER (not just ENTER)

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hey there. If there are only 5 numbers at some point, the 5 and 10 would
be
the same. I hope that helps. Basically, over the course of 3 or so months,
these numbers will begin to be added to the rows and by the end, there
will
be somewhere around 30 numbers out of 40 potential leaving 10 random
spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.

Thanks

"T. Valko" wrote:

What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and last
10
numbers in a row of up to 40 numbers. There will be various random
spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each have
a
few
spaces between them. There will be no 0's or negatives in the data.

Thanks







T. Valko

Complex Averages
 
You're welcome. Thanks for the feedback!

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Thanks Biff, that worked great. I appreciate your time on this.

KJ

"T. Valko" wrote:

Hmmm...

Well, let's start with this and go from there.

This will average the last 5 numbers in the range A1:J1.

Array entered** :

=AVERAGE(J1:INDEX(A1:J1,LARGE(IF(ISNUMBER(A1:J1),C OLUMN(A1:J1)-MIN(COLUMN(A1:J1))+1),5)))

If there are less than 5 numbers the formula will return a #NUM! error.

** array formulas need to be entered using the key combination of
CTRL,SHIFT,ENTER (not just ENTER)

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hey there. If there are only 5 numbers at some point, the 5 and 10
would
be
the same. I hope that helps. Basically, over the course of 3 or so
months,
these numbers will begin to be added to the rows and by the end, there
will
be somewhere around 30 numbers out of 40 potential leaving 10 random
spaces
in each column assuming 40 max. So the last 5 and last 10 averages will
develop and deviate as more data is entered.

Thanks

"T. Valko" wrote:

What should happen if there aren't 5 or 10 numbers to average?

--
Biff
Microsoft Excel MVP


"kjal" wrote in message
...
Hello, I need to design a spreadsheet that averages the last 5 and
last
10
numbers in a row of up to 40 numbers. There will be various random
spaces
between the entered numbers. So for example, if there are 15 numbers
spread
over 40 rows, I would need to average the last 5 which could each
have
a
few
spaces between them. There will be no 0's or negatives in the data.

Thanks










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