# How to subtract averages accurately

Group A includes 20 students who took an exam and their grade mean was 28(±9.15).

After taking the second exam, their mean grade has decreased by 14(±9.9) in comparison with the first exam.

My question is: How to find the average score of their second exam if it not given?

I know that I can subtract the averages and get an estimate of their second exam average. However, I would like to know how to get the most accurate average, and whether the SD has any use in this process.

• For the average you can just add/subtract them and it will give you the exact answer, SD is not relevant here. Dec 2, 2022 at 11:25
• The problem is that I also need the standard deviation of the second exam's grade mean. How do I get it? Dec 2, 2022 at 12:38
• Ok, the average estimate is 28-14=14: you can't do better than that (unless you know that some observations are not reliable and should thus be given less weight). To calculate SD, however, you need the correlation between the two exams. Dec 2, 2022 at 13:22
• Do you have the data for each student? Is this a homework exercise? Dec 3, 2022 at 16:02