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A sampling distribution of sample means is a distribution that shows the means from all possible samples of a given size. Let’s start with an example of a sampling distribution.
Consider the spinner shown here:
Suppose you spin it four times to obtain an average. You get a 2 the first time, a 4 the second time, a 3 the third time, and a 1 the fourth time. The mean is the average of 2, 4, 3, and 1 is:
So, your first mean is 2.5.
Sample | Mean |
---|---|
S1 = {2, 4, 3, 1} | x̄1 = 2.50 |
However, your mean won't be 2.5 every time. Suppose you repeat this process five more times to get the following six samples:
Sample | Mean |
---|---|
S1 = {2, 4, 3, 1} | x̄1 = 2.50 |
S2 = {1, 4, 3, 1} | x̄2 = 2.25 |
S3 = {4, 2, 4, 4} | x̄3 = 3.5 |
S4 = {2, 2, 3, 1} | x̄4 = 2.00 |
S5 = {3, 1, 1, 1} | x̄5 = 1.50 |
S6 = {1, 1, 1, 2} | x̄6 = 1.25 |
So how can we represent all these distributions?
Source: THIS TUTORIAL WAS AUTHORED BY JONATHAN OSTERS FOR SOPHIA LEARNING. PLEASE SEE OUR TERMS OF USE.