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Unformatted text preview: Sullivan Fundamentals of Statistics , 2nd Edition Chapter 3 Slide 1 of 69 Chapter 3 Overview Three characteristics of a quantitative variable's distribution: Shape Visually via graphs. Center (Typical Value) Numeric summary. Spread (Dispersion) Numeric summary. Appropriate measures of center and spread depends upon the distribution's shape. Chapter 2 Chapter 3 Sullivan Fundamentals of Statistics , 2nd Edition Chapter 3 Slide 2 of 69 Review: Populations vs. Samples Analyzing populations versus analyzing samples. For populations: We know all of the data. Descriptive measures of populations are called parameters . Parameters are often written using Greek letters ( ). For samples: We know only part of the entire data. Descriptive measures of samples are called statistics . Statistics are often written using Roman letters ( ). x Sullivan Fundamentals of Statistics , 2nd Edition Chapter 3 Slide 3 of 69 Chapter 3, Section 1 (Outline) Measures of Central Tendency Numeric values that represent the average or typical value of a quantitative variable. The arithmetic mean of a variable. The median of a variable. The mode of a variable. Identifying the shape of a distribution using the mean, median, and mode. Sullivan Fundamentals of Statistics , 2nd Edition Chapter 3 Slide 4 of 69 Central Tendency The arithmetic mean of a variable is often what people mean by the average add up all the values and divide by the number of measurements in the data set. To compute the arithmetic mean of: 6, 1, 5 Add up the three numbers and divide by 3. (6 + 1 + 5) / 3 = 4.0 The arithmetic mean is 4.0, one more decimal place than the data. General Rounding Rule for Reporting Statistics One interpretation: The arithmetic mean can be thought of as the center of gravity where the yardstick balances. (p. 109110) Sullivan Fundamentals of Statistics , 2nd Edition Chapter 3 Slide 5 of 69 Review: Summation Notation Used to simplify summation instructions: Each observation in a data set is identified by a subscript: x 1, x 2, x 3, x 4, x 5, . xn Notation used to sum the above numbers together is: 1 2 3 4 1 n i n i x x x x x x + + + + + = = L 2 1 n i i x = 2 1 n i i x = & Is the same as ? Data set: 1, 2, 3, 4 4 2 2 2 2 2 1 2 3 4 1 1 4 9 16 30 i i x x x x x = = + + + = + + + = ( 29 2 4 2 2 2 1 2 3 4 1 1 2 3 4 10 100 i i x x x x x = = + + + = + + + = = & Sullivan Fundamentals of Statistics , 2nd Edition Chapter 3 Slide 6 of 69 Arithmetic Mean The mean is an arithmetic average of the elements of the data set. The mean of a sample of n measurements is denoted by and equals: If the data are from a population , the mean is denoted by (mu) and equals: 1 i N i x N = = N = Population Size n = Sample Size 1 i n i x x n = = x statistic parameter Sullivan Fundamentals of Statistics , 2nd Edition Chapter 3 Slide 7 of 69...
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