There are 3 students that make up the total population of Summer Calculus students at ACM. Their grades on the first test were 54, 41, 62.
a) What is the mean of this population?
b) What is the variance of this population?
c) What is the standard deviation of this population?
d) Every possible sample of 2 of these students is listed below.
Complete the table.
Ages |
Sample mean, ¯xx¯ |
|---|
54, 54 |
|
54, 41 |
|
54, 62 |
|
41, 54 |
|
41, 41 |
|
41, 62 |
|
62, 54 |
|
62, 41 |
|
62, 62 |
|
e) What is the the mean of all the sample means?
This shows that the mean of all the sample means equals the population mean.
f) What is the the standard deviation of all the sample means?
g) What is the standard error, σ√nσn where σσ is the population standard deviation and nn is the sample size?
This shows that the standard error equals the standard deviation of all the possible sample means.