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.AgesSample 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.

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved. a) The population mean is, μ=∑iXN=54+41+623=1573=52.3333 Thus, the population mean is 52.3333.b) The population variance is, σ2=∑iX-μ2N=54-52.33332+41-52.33332+62-52.333323=2.7779+128.4437+93.44513=224.66673=74.8889 Thus, the population variance is 74.8889.c) The population standard deviation is, σ=σ2=74.8889=8.6538 Thus, the population standard deviation is 8.6538.

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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