A sampling Distribution oF sample means:    The number of times 4 people go grocery shopping in a month is given by the population values {1,3,5,7}.  You randomly choose two of the four people, with replacement.  List all possible samples of size n=2 and caclculate the mean of each.  These means form the sampling distribution of the sample means.  Find the mean, variance, and standard deviation of the sample means.  Compare your results with the mean = 4, variance = 5, and standard deviation = 2.2.    I know how they obtained the mean but using the formula  to get variance  I am not sure how they go 5/2 = 2.5.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Hello, 

I am having troubles with Example 1 in the elementary statistics book in Chapter 5.4

 

A sampling Distribution oF sample means: 

 

The number of times 4 people go grocery shopping in a month is given by the population values {1,3,5,7}.  You randomly choose two of the four people, with replacement.  List all possible samples of size n=2 and caclculate the mean of each.  These means form the sampling distribution of the sample means.  Find the mean, variance, and standard deviation of the sample means.  Compare your results with the mean = 4, variance = 5, and standard deviation = 2.2. 

 

I know how they obtained the mean but using the formula  to get variance  I am not sure how they go 5/2 = 2.5.  

 

 

Thank you.  

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