Chapter 3

Chapter 3 - Chapter 3 Descriptive Statistics Numerical...

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Chapter 3 Descriptive Statistics Numerical Methods
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Our goal? Numbers to help us answer simple questions. ± What is a typical value? ± How variable are the data? ± How extreme is a particular value? ± Given data on two variables, how closely do they move together?
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Measures of Central Tendency Here are three ways to identify a “typical” observation ± Mean – the arithmetic average ± Median – the middlemost value ± Mode – the most common value
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There are formulas, but . . . One confusing thing about the formulas is all the notation they use. To explain why we need the notation, and why you need to know it, let me remind you of an important distinction . . .
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Population vs. Sample ± A population is the set of all data that characterize some phenomenon, and a number computed from population data is called a parameter . ± A sample is a subset of a population, and a number computed from sample data is called a statistic .
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An Example ± Population - All registered voters. ± Parameter – The fraction of all registered voters who prefer John McCain to Barack Obama. ± Sample – 2500 voters surveyed by Gallup. ± Statistic – The fraction of voters in the poll who prefer McCain to Obama.
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Another Example ± Population - All Duracell AA batteries. ± Parameter – The average lifetime of all Duracell AA batteries in a particular toy. ± Sample – A hundred batteries being tested by the manufacturer. ± Statistic – The average lifetime of the 100 tested batteries in the particular toy.
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Why is the distinction important? ± Sample statistics are very different from population parameters. Parameters are fixed numbers. Before the sample is drawn, statistics depend on the elements that may be selected, and are random. ± Once a sample is drawn, the numbers themselves are likely to be different; that is 48% of the population but 51% of the sample may prefer Obama. ± Therefore, our notation must clearly distinguish sample statistics from population parameters.
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Now let us return . . . To those measures of central tendency.
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The Sample Mean ± The sample mean is the arithmetic mean of some sample data. ± The notation for a sample mean is X-bar. ± The notation for sample size is a lower case n. 1 n i i x X n = =
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The Population Mean ± The population mean is the arithmetic mean of some population data. ± The notation for a population mean is the Greek letter mu. ± The notation for population size is an upper case N. 1 N i i x N µ = =
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And THIS is the summation operator Here it is just telling us to add the observations. 123 1 n in i xx x = = ++ + "
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Don’t be intimidated by the summation operator ± It is just shorthand; it saves space. ± The summation operator is just the Greek letter Sigma. ± Sigma is Greek for S, and S stands for Sum.
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This note was uploaded on 03/01/2012 for the course ECON 371 taught by Professor Staff during the Spring '08 term at UVA.

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Chapter 3 - Chapter 3 Descriptive Statistics Numerical...

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