Indirect Average of unspecified length array of differences - excel

Question

I have the following indirect reference:
=AVERAGE(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3))
On 'Pages'!D3 I have another page '1D_3' and on 'Pages'!J3 I have 2:2.
I need to alter the above code to instead find the average of the differences between each successive value. I can only change the value in 'Pages'!J3 (2:2) and I can change the equation above.
From this reference http://www.excelforum.com/excel-general/742194-difference-between-consecutive-number.html I have come up with how I can do the difference between each successive, but only if I have a known range. Ex. For elements A1:G1,
=SUM(A1:F1-B1:G1)
I could then do the following for the average:
=SUM(A1:F1-B1:G1)/(COUNT(1:1)-1)
But I do not know how to do the SUM part if I have an unspecified range. I also am unsure of how to implement this in the INDIRECT function.
Just some additional background info that may clarify this, The values in the array are times from a stopwatch. It was assumed that each value would be a time difference, but instead it is just the time on the stopwatch (Ex. 0.0015, 1.0034, 2.356, etc.). I want to find the average time duration between each value.
Any help would be greatly appreciated.

Answer 1

Before solving the formula you seek, let me just point out that all you need is the (EndValue-StartValue)/NumberOfEntries - no need to calculated the difference of each timing point first, as this will cancel itself out in the final calculation anyway.
Now assuming that Pages!J3 still only contains the row number, i.e. the formula =INDIRECT("'" & Pages!D5 & "'!" & Pages!J3) will return you a reference to this row. In the following formula, I use X as an replacement for the INDIRECT formula, to make it more readable:
=(OFFSET(X,0,0,1,1)-OFFSET(X,0,COUNT(X),1,1))/COUNT(X)
Now you only need to replace X with the above formula - or simply add a named range with the formula. If you combine it, you'll end up with this formula:
=(OFFSET(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3),0,0,1,1)-OFFSET(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3),0,COUNT(X),1,1))/COUNT(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3))

Answer 2

I tried what the other poster suggested and it did not work, even when replacing the remaining 'X'. I worked through a few other examples in Excel to finally come to the following conclusion. To not let this be lost to the sands of the internet, I decided to post my own solution. So I wanted an average of the differences between time values. Essentially, I wanted a sum over the total number of times (mean). The difficulty was in the indirect referencing and INDIRECT referencing within an INDIRECT reference.
So what I had was data on multiple worksheets, pages (Pages on B through E columns) and ranges (Pages on J column) on another worksheet, and the resulting operations on another sheet.
=SUM(INDIRECT("'"&Pages!D5&"'!C2"):INDIRECT("'"&Pages!D5&"'!"&SUBSTITUTE(ADDRESS(2,COUNTA(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3)),4),"1",""))-INDIRECT("'"&Pages!D5&"'!B2"):INDIRECT("'"&Pages!D5&"'!"&SUBSTITUTE(ADDRESS(2,COUNTA(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3))-1,4),"1","")))/(COUNT(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3))-1)
To break this into parts, we have:
=SUM(junk)/COUNT(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3))-1
And the 'junk' part is as follows. Ultimately, it was in the form:
=SUM(A1:F1-B1:G1)
Without INDIRECTs, if we had a page of data named '8D_2FU':
=SUM('8D_2FU'!C2:AW2-'8D_2FU'!B2:AV2)/(COUNT('8D_2FU'!2:2)-1)
Note that for this implementation we pick a maximum column on AW which was fine for all possible datasets.
There is also one more part of interest in the 'junk'. You cannot make an INDIRECT reference within an INDIRECT reference, so to fool Excel, we can use the SUBSTITUTE command and get the same result by converting the address contained in the INDIRECT reference.
SUBSTITUTE(ADDRESS(2,COUNTA(INDIRECT("'" & Pages!D5 & "'!" & Pages!J3)),4),"1",""))
Finally, to use this, you must make this an array operation by instead of typing 'Enter' you must type, CTRL+SHIFT+Enter. The result was also confirmed using a brute force test case.