How should I aggregate data across multiple periods


I am trying to figure out the best way to aggregate data and am unable to find anything in the literature (e.g., Google or this site) to give me a reason to choose one method of aggregation over another (or to explain how aggregation might impact results). I have data that are gathered each month. I want to compare a base line of months 1 – n to month n + 1 (an event occurs at the end of month n for which I want to see if the event impacts production). How best can I aggregate the data from months 1 – n? Should I sum the data or average it?

For example, given the following data, I want to know if M5 is significantly different from what happened in months 1-4.

Product M1 M2 M3 M4 || M5
Product 1 25 30 27 24 || 29
Product 2 8 12 16 13 || 17
Product 3 13 11 12 15 || 13
Product 4 8 6 9 10 || 9
Product 5 12 13 10 12 || 14
Product 6 20 19 22 24 || 24

Should I sum months1-4 or average them? Or is there some other form of aggregation I should use?

First, if I want to run a paired t-test to compare months 1-4 against month 5, seems to me that I need to use an average because summing the data would by definition cause the means to be different. Does averaging have some deleterious effect that will invalidate the results?

Second, when running a Chi-square test, I get differ p-values for sum versus average, but I am not sure how to interpret the difference.