Sampling distribution of means question

[LoveStruck16]

Question: there are 5 x 5 = 25 different samples of two scores (n=2) that can be drawn from the population. One would be (2, 2); another (2,3); another (2,6); and so on. List all of the possible sample means.

So i ended up getting..

a) Let's say that there were 25 occurrences of score_1 and 0 occurrences of score_2

Then i'd have [(25 * score_1) + (0 * score_2) ] / 25 = score_1 as a possible sample mean.

Let's say that there were 24 occurrences of score_1 and 1 occurrence of score_2

Then i'd have [(24 * score_1) + (1 * score_2) ] / 25 as a possible sample mean.

Let's say that there were 23 occurrences of score_1 and 2 occurrences of score_2:

Then i'd have [(23 * score_1) + (2 * score_2) ] / 25 as a possible sample mean.

and so forth until I have:

[(1 * score_1) + (24 * score_2) ] / 25.

and finally:

[(0 * score_1) + (25 * score_2 ] / 25 = score_2

So in all, I'll end up with 26 possible sample means.

but the next question from these are:

b) compute the mean of your sampling distribution of means
c) compute the standard deviation of your sampling distribution of means
d) compute the theoretical value for the standard error of the mean (central limit theorem "shortcut")

So How would I compute the mean of my sampling distribution of means?

 

[tkhunny]

Hint.
1+2+3+...+25=??