xid-2443986_1 - Describing Data (part two) Timothy S....

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Describing Data (part two) Timothy S. Sullivan, Ph.D. MS 251: Statistical Analysis for Business Decisions Southern Illinois University Edwardsville Last update: August 26, 2009
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Population • A population is the set of observations that a researcher is studying. • Statisticians typically use N to denote the number of objects in a population. • For example: • all SIUE students • all employees of Anheuser-Busch.
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Parameter • A parameter is a descriptive measure of a population. • Statisticians often use θ to denote a generic parameter.
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Census • A census is the process of collecting information from all of the members of a population. • Taking a census to calculate a parameter is often impractical: • Taking a census is often time-consuming. • Taking a census is often expensive. • Taking a census is sometimes impossible.
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Sample • A sample is a subset of a population. • Statisticians typically use n to denote the number of observations in a sample.
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Statistic • A statistic is a descriptive measure of a sample. • Statisticians often use to denote a generic statistic. • Analysts often use statistics to estimate parameters. θ ˆ
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Central tendency A first step in describing a variable is to measure its middle and typical values. These are sometimes described as the variable’s central tendency . • We will use four measures: • mean, • median, • mode, • proportion.
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Population mean • The population mean of the variable x is • The x subscript indicates which variable’s mean we’re measuring (in case there is more than one variable). N x N x x x μ N i i N x = = + + + = 1 2 1
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Population mean is what we normally call the average. is a population parameter. is also known as the first moment of the population. is also known as the expected value of x. When using this term we usually use the notation E(x). x μ x μ x μ x μ
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Population mean does not need to be an observed value in the population. does not need to be an observable value in the population. is only meaningful for quantitative data. x μ x μ x μ
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Properties of the population mean • If x and y are variables, and c is a constant, the following properties apply. • E(x+c) = E(x) + c • E(cx) = cE(x) • E(x+y) = E(x) + E(y) • E(x y) may or may not equal E(x) E(y)
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In-class exercise • A restaurant has three waiters and waitresses. They earn $5.50, $6.00 and $6.50 an hour. • What is the mean wage of this population?
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• A restaurant has three waiters and waitresses. They earn $5.50, $6.00 and $6.50 an hour. • Suppose each worker receives a 50-cent-an-
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xid-2443986_1 - Describing Data (part two) Timothy S....

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