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# General Statistics on Population

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Problem: Please accept only if willing to explain.
A POPULATION consists of these values: 2,3,6,8,11,18.
a) Find Mean and Standard Deviant
b) List all samples of size n=2 that are obtained without replacement.
c)Find the population of all values of the mean of the values in a sample by finding mean of each sample from part b.
d) Find the mean (U subscript mean of the values in a sample)of the population of all samples
e) Verify.

##### Solution Summary

Problem: Please accept only if willing to explain.
A Population consists of these values: 2,3,6,8,11,18.
a) Find Mean and Standard Deviant
b) List all samples of size n=2 that are obtained without replacement.
c)Find the population of all values of the mean of the values in a sample by finding mean of each sample from part b.
d) Find the mean (U subscript mean of the values in a sample)of the population of all samples
e) Verify.

##### Solution Preview

Solution. Denote the mean and standard deviation by , respectively. Then we have

Attached is a table by using Excel

Column1

Mean 8
Standard Error 2.408319
Median 7
Mode #N/A
Standard Deviation 5.899152
Sample Variance 34.8
Kurtosis 0.696591
Skewness 0.990791
Range 16
Minimum 2
Maximum 18
Sum 48
Count 6

b) List all samples of size n=2 ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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