Answered: The following table shows the number of…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section11.4: Two-ways Tables

Problem 5E

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The following table shows the number of active military personnel in 2009, by reglon (including the District of Columbia). 229,834 Mountain 89,816 West South Central 177,336 Pacific West North Central 64,564 East North Central 26,384 East South Central 68,440 South Atlantic 376.034 Middle Atlantic 4 41,441 New England 8,579 Source: U.S. Census Bureau, Statistical Abstract of the United States: 2012, Table 508 (data) and U.S. Census Bureau, Census Regions and Divisions of the United States (regions) a. Calculate the mean and standard deviation for the population. b. Now take 10 samples of size 3 from the population. Use either simple randonm sampling or systematic sampling with the help of the table of random numbers in Appendix A. Calculate the mean for each sample. c. Once you have calculated the mean for each sample, calculate the mean of means (ie., add up your 10 sample means and divide by 10). How does this mean compare with the mean for all states? How does the value of the standard deviation that you calculated in Exercise 8a compare with the value of the standard error (ie., the standard deviation of the sampling distribution)? d. Construct two histograms, one for the distribution of values in the population and the other for the various sample means taken from Exercise 8b. Describe and explain any differences you observe between the two distributions e. f. It is important that you have a ciear sense of the population that we are working with in this exercise. What is the population?

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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