Consider all possible samples of size 3 that can be drawn without replacement from the population 1, 5, and 8, 6, 10. Compute the following:
1. Population mean
2. Population variance
3. Population standard deviation
4. Illustrate the probability histogram of the sampling distribution of the means
Given population = 1, 5, 8, 6, 10
Population mean "\\mu =\\dfrac{1+5+8+6+10}{5}=\\dfrac{30}{5}=6"
Population variance
"\\sigma^2= \\sum \\dfrac{ (x-\\mu)^2}{n}=\\dfrac{(1-6)^2+(5-6)^2+(8-6)^2+(6-6)^2+(10-6)^2}{5}=\\dfrac{46}{5}=9.2"
Population standard deviation "\\sigma=\\sqrt{ Variance}=\\sqrt{9.2}=3.033"
All possible samples and their means:
Sampling distribution of the sample mean:
Probability histogram of the sampling distribution of the means:
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