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# ch3_outline - Chapter 3 Outline Introduction What is an...

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Chapter 3 Outline Introduction What is an average? It is a single number used to describe the central tendency of a set of data. Examples of an average are: The average length of the school year for students in public schools in the United States is 180 days. The median household income for the United States was \$44,389 in 2004, the most recent year for which this data is available ( http://www.cens us .gov ). The median selling price for a single-family home in Boston in August, 2005 was \$375,000 ( The Boston Globe, October 26, 2005 ). The mean wage for accountants was \$24.56 per hour in 2004. ( The Census Bureau’s Income Statistics Branch , July, 2005 ). Computer Software Engineers’ pay averaged \$38.44 per hour, while Library Technicians averaged \$12.22 per hour. ( Bureau of Labor Statistics web site: http://stats.bls.gov, July, 2005 ) There are several types of averages. We will consider five: the arithmetic mean, weighted mean, the median, the mode, and the geometric mean. Measures of Location The purpose of a measure of location is to pinpoint the center of a set of observations. Measure of location : A single value that summarizes a set of data. It locates the center of the values. The arithmetic mean, or simply the mean, is the most widely used measure of location. Mean : The sum of observations divided by the total number of observations. The population mean is calculated as follows: Population mean = Sum of all values in the population Number of values in the population In terms of symbols, the formula for the mean of a population is: Population Mean X N [ ] 3 1 Where: μ represents the population mean. It is the Greek letter “mu.” N is the number of items in the population. X is any particular value. indicates the operation of adding all the values. It is the Greek letter “sigma.” X is the sum of the X values. [3-1] indicates the formula number from the text. Any measurable characteristic of a population is called a parameter . Paramete r: A characteristic of a population.

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The Sample Mean As explained in Chapter 1, we frequently select a sample from the population to find out something about a specific characteristic of the population. The mean of a sample and the mean of a population are computed in the same way, but the shorthand notation is different. In terms of symbols, the formula for the mean of a sample is: Sample Mean X X n [ ] 3 2 Where: X is the sample mean; it is read as “ X bar”. n is the number of values in the sample. X is a particular value. indicates the operation of adding all the values. X is the sum of the X values. [3-2] is the formula number from the text. The mean of a sample, or any other measure based on sample data, is called a statistic . Statistic : A characteristic of a sample. “The mean weight of a sample of laptop computers is 6.5 pounds,” is an example of a statistic.
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ch3_outline - Chapter 3 Outline Introduction What is an...

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