Summing really is not a great approach unless the summed scores are scaled in a way that’s well known in application (and even then is problematic).

The mean has two advantages. 1) If the items have a fixed range interpretation is usually easier. If it’s a 1 to 7 scale then 1 is lowest, 7 highest and 4 in the middle. A summed scale is hard to interpret because of variation in number of items. 2) With missing items the sum treats missing as zero so it distorts the score. The mean treats them as if missing completely at random. This is not perfect but better than treating values as 0. Also with only a few missing items and problems are minor.

Ideally one would impute missing values but I’ve seen quite a few analyses that sum scores with missing data and end up with essentially garbage outcomes (if 0 is an impossible value it can really mess with results).

If there’s no missing data the analyses will be identical except for the interpretation issue. So generally the mean is the better and safer default.

SPSS provides several ways of adding or averaging items (X1, X2, …, Xk).

If you compute: X total = X1 + X2 + … Xk, X total will have a system missing value if one or more of the X scores are system missing.

If you compute X total = SUM(X1, X2, …., Xk), X total will be the sum of scores for all non-missing items. The problem with this is that the sum will be small for people who are missing one or several items; you won’t know how many items are included in the sum for each person unless you look at the lines of data.

If you compute X mean= MEAN(X1, X2, …,Xk) X total is the mean of scores across all non missing items. If you want to convert X mean into what the sum of scores across all items would have been without any items missing, multiply X mean by k, the number of test items.

I agree that when you use a standard measure you should use the scoring method provided by the test developers. However, even when you do that, you need to be careful which of these three ways you choose to combine items. If I want the sum of scores across all items I prefer to use the Mean function and multiply by k.

(There are more sophisticated ways to deal with missing values, but I think that is beyond the scope of your question.)

Assuming no missing items, the sum of the Xs will correlate 1.0 with the mean of the Xs. For purposes of correlation and regression it doesn’t matter whether you use the sum or the mean. Of course M SD differ for the sum versus the mean of all items, and you will want these to be in the same units that are reported by other authors.

If you have any reverse-scored or reverse-worded items be sure to recode them before you sum or average scores. Test scoring instructions will tell you if this is needed.

Adding to Tarek Abd Elhamid Taha's example about getting a prorated sum when some items are missing, suppose you have 10 items (X1 to X10), all on the same scale (e.g., 1-5), and with no need for reverse-coding any items. But suppose too that not everyone has complete data. And suppose you want to compute a prorated sum of the items, but only for Ss who have at least 7 items. (That 7 is an arbitrary number I just made up to make the example concrete.) You can do this in SPSS:

COMPUTE MySum = MEAN.7(X1, X2, ..., X10) * 10.

The .7 on MEAN.7 tells SPSS to only return a valid (non-missing) result if at least 7 of the variables have valid data. (This type of suffix also works on other functions, like SUM, btw.)

As I noted above, this type of sum is often called a prorated sum. But it is the same result you would get via (within-subject) mean imputation for the missing values. And as you know, nowadays, mean-imputation is not considered a great way of dealing with missing data, although this approach may still be recommended in scoring instructions for various instruments. HTH.