I have one column with numbers eg. 130, 131, 135, 140, 120.., I would like to find the differences eg. 131130, 135131, 140135.. and find their average without using another column to find the differences and then the average. Is there a formula to do that all together.

Are you looking for multiple outputs (differences & average)? Is the average you're looking for the average of the list values or the average of the differences?– fixer1234Aug 31, 2015 at 16:18

Average of the differences– Spongebob SquarepantsAug 31, 2015 at 16:20

1All but the first and last values cancel each other out when you add up the differences to find the average. The average of the differences is (last value  first value)/(count of values  1).– fixer1234Aug 31, 2015 at 16:26
3 Answers
You're overthinking this:
(131130) + (135131) + (140135) + ...
= 131  130 + 135  131 + 140  135 + ...
= 130 + 131  131 + 135  135 + 140 ...
= 130 + (131131) + (135135) + ...
= 130 + 0 + 0 + ... + 120
= 120130
i.e., the sum of the differences between pairs of consecutive numbers is simply the difference between the last number and the first one. To get the average, just divide that by the number of pairs, which is the number of numbers minus 1.
So, for example, if the numbers are in A1
... A7
, you can say
=(A7A1)/6
or
=(A7A1)/(ROWS(A1:A7)1)
or
=(A7A1)/(ROW(A7)ROW(A1))
(Note that you don't need to say 1
in the last form.)

2For the average difference, you need n1 rather than n (there's n1 differences). Aug 31, 2015 at 16:45

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This method is overkill in this case, but you could also do this with an array formula:
=AVERAGE((A2:A7)(A1:A6))
To enter an array formula, type it in, then, with your cursor still in the formula editing field, press the combinationCtrl+Shift+Enter. The formula should now should show up as
={AVERAGE((A2:A7)(A1:A6))}
...but you can't type those curly braces in yourself  you have to use the keycombo.
How it works:
As an array formula, (A2:A7)(A1:A6)
returns an array (list) of each of the differences: A2A1, A3A2, etc. This is wrapped in an AVERAGE()
and voilà.
The observation about most of the values cancelling out that @fixer1234 pointed out in a comment and @Scott explained in his answer is the best approach for your particular problem. As Scott noted in a comment below, you could do something similar with =AVERAGE(A2:A7)AVERAGE(A1:A6)
. This would also take advantage of various terms calculating each other out.
The array formula approach in this answer does not rely on cancellation at all  it actually calculates each difference and finds the average of them. This is unnecessary for your exact scenario, but could serve as a building block if your requirements become more complex.

1(1a) I believe that you have a sign error. The OP appears to be asking for the average of A2A1, A3A2, ..., so your answer should be
=AVERAGE((A2:A7)(A1:A6))
. (1b) You don't actually need the extra parentheses; you can say=AVERAGE(A2:A7A1:A6)
. Arguably, the extra parentheses may make it clearer. (2) You don't need an array formula; just do=AVERAGE(A2:A7)AVERAGE(A1:A6)
. (3) While I certainly figured this out by myself, and didn't copy from anybody, we should recognize the fact that fixer1234 was the first to post the observation about most of the values cancelling out. Aug 31, 2015 at 17:17
It's been a long time since my last Statistics course, but it sounds like you're looking for the average deviation, correct?
Try =AVEDEV()
Another option would be to go ahead and use another column and hide it.