Example The following table gives the Fall 2011 final grades of a class of four

# Example the following table gives the fall 2011 final

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ExampleThe following table gives the Fall 2011 final grades of a class of four students.Allan100James90Barbara70Nicolas80Sum=340The mean isμ=3404=85.Now, consider the following table of all possible averages of grades ofgroupsof size 2.Group of size 2average grade(meanx)The mean of these averages isμx=510 Allan & James 95 Allan & Barbara 85 Allan & Nicolas 90 James & Barbara 80 James & Nicolas 85 Barbara & Nicolas 75 Sum=510 6 = 85 . This table represents the sampling distribution of the mean of samples of size 2 . A. Bourhim (Syracuse University) Sampling Distributions and The Central Limit Theorem MAT121, Spring 2015 4 / 9
Example (Continued)Now, consider the following table of all possible averages of grades ofgroupsof size 3.Group of size 3average grade(meanx)Allan & James & Barbara86.67Allan & James & Nicolas90Allan & Barbara & Nicolas83.33James & Barbara & Nicolas80Sum=340The mean of these averages isμx=3404=85.This table represents the sampling distribution of the mean ofsamples ofsize 3. A. Bourhim (Syracuse University)Sampling Distributions and The Central Limit Theorem MAT121, Spring 2015 5 / 9
Properties The mean of all sample means coincides with the population mean.