# “difference of average [something] between the different [something]”?

I have this rather complicated expression that I would like to express in the most understandable way possible.

The difference of average [something] between the different [something].

I am comparing things by their difference of the average of some metric. I feel that the way I express this is complicated, and I would like to express it in a simpler way.

The problem here is that I can't just say "the average [something] difference between" because it is not the difference that is averaged, and it is important to make that evident.

Is there some other way to more concisely express what I want to say?

The difference between the averages of A and B.

First, 'the averages of' or 'the average of', just to emphasize you're talking about the averages, not some average differences, then the clear way of expressing is: "you measure difference between the averages". The way you try to express it "measure difference in averages between A and B", while correct, is really obscuring the meaning.

I believe you are referring to 'standard deviation'. This is a mathematical concept that expresses the degree to which the individual items in a set of data differ from the average (mean) of that set of data, i.e. the degree of 'spread'.

For example, consider these two data sets:
A. {1,3,5,7,9}
B. {3,4,5,6,7}
Both sets have 5 items and a mean of 5. But set A has a wider spread, and the degree of spread can be quantified by giving its standard deviation (s.d.) Set A's s.d. is 3.16 and set B's s.d. is 1.58. A standard deviation can be calculated for any set of data, and the data need not be evenly spread.

If this is what you are trying to express, you can look up the methodology for calculating standard deviation. All spreadsheet programs will have a suitable formula function.

I am a statistician. If you can put this into a formula, I can translate it back into English (unfortunately ELL doesn't seem to have LaTeX compatibility, so typing formulas is hard). It might be standard deviation, but I think it might be mean absolute deviation (which isn't a common thing to compute - usually it would be median absolute deviation).

The standard deviation involves squaring the differences, summing those squares and then taking the square root of the sum. The median absolute deviation involves taking the median of the absolute value of the differences.

• no, not the average difference, the difference of the averages as SF correctly answered. I am talking about two distributions, and the difference between their means. Since you are a statistician: What is a better way to compare to distributions, possibly without having to assume they are normal? – kutschkem Sep 19 '13 at 11:13
• This would be better asked on the statistics site (CrossValidated) but quantile quantile plots are good. Or parallel box plots. – Peter Flom Sep 19 '13 at 11:19