hi i need help calculating the standard error using the central limit theorem.

*a population of scores contains exactly 5 scores : 2, 3, 6, 8, 11, there are 5x5=25 samples of the two scores (n=2)*

i already calculated the standard deviation and mean. for the question my standard deviation was 3.6742 and my mean was 6.

i also need to calculate the standard deviation of the following sampling distribution of means. apparently this is the longhanded way of calculating standard error.

(2, 2) ... 2
(2, 3) ... 2.5
(2, 6) ... 4
(2, 8) ... 5
(2, 11) ... 6.5
(3, 2) ... 2.5
(3, 3) ... 3
(3, 6) ... 4.5
(3, 8) ... 5.5
(3, 11) ... 7
(6, 2) ... 4
(6, 3) ... 4,5
(6, 6) ... 6
(6, 8) ... 7
(6, 11) ... 8.5
(8, 2) ... 5
(8, 3) ... 5,5
(8, 6) ... 7
(8, 8) ... 8
(8, 11) ... 9.5
(11, 2) ... 6,5
(11, 3) ... 7
(11, 6) ... 8,5
(11, 8) ... 9,5
(11, 11) ... 11

thank you :)

If you already have the Standard Deviation (SD),

SEm(Standard Error of the mean) = SD/√(n-1)

I don't understand the meaning of the numbers in parentheses.

To calculate the standard error using the central limit theorem, you need to follow these steps:

Step 1: Find the mean of the population. In this case, you mentioned that the mean is 6.

Step 2: Calculate the standard deviation of the population. You mentioned that the standard deviation is 3.6742.

Step 3: Calculate the standard deviation of the sampling distribution of means using the formula:
Standard Error = (Population Standard Deviation) / √(Sample Size)

In this case, the sample size is 2. So, the standard error would be:

Standard Error = 3.6742 / √2 ≈ 2.597

Therefore, the standard error of the sampling distribution of means is approximately 2.597. This measures the average distance between the sample means and the population mean. It tells us the spread or variability of the distribution of sample means.