Lecture Business statistics in practice (7/e): Chapter 3 - Bowerman, O'Connell, Murphree

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Chapter 3 - Descriptive statistics: Numerical methods. After mastering the material in this chapter, you will be able to: Compute and interpret the mean, median, and mode; compute and interpret the range, variance, and standard deviation; use the Empirical Rule and Chebyshev's Theorem to describe variation;...

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Nội dung Text: Lecture Business statistics in practice (7/e): Chapter 3 - Bowerman, O'Connell, Murphree

Chapter 3 Descriptive Statistics: Numerical Methods McGrawHill/Irwin Copyright © 2014 by The McGrawHill Companies, Inc. All rights reserved.
Descriptive Statistics 3.1 Describing Central Tendency 3.2 Measures of Variation 3.3 Percentiles, Quartiles and Boxand Whiskers Displays 3.4 Covariance, Correlation, and the Least Square Line (Optional) 3.5 Weighted Means and Grouped Data (Optional) 3.6 The Geometric Mean (Optional) 32
LO3-1: Compute and interpret the mean, median, and mode. 3.1 Describing Central Tendency  In addition to describing the shape of a distribution, want to describe the data set’s central tendency ◦ A measure of central tendency represents the center or middle of the data ◦ Population mean (μ) is average of the population measurements  Population parameter: a number calculated from all the population measurements that describes some aspect of the population  Sample statistic: a number calculated using the sample measurements that describes some aspect of the sample 33
LO3-1 Measures of Central Tendency Mean, The average or expected value Median, Md The value of the middle point of the ordered measurements Mode, Mo The most frequent value 34
LO3-2: Compute and interpret the range, variance, and standard 3.2 Measures of Variation deviation. Knowing the measures of central tendency is not enough Both of the distributions below have identical measures of central tendency Figure 3.13 35
LO3-2 Measures of Variation Range Largest minus the smallest measurement Variance The average of the squared deviations of all the population measurements from the population mean Standard The square root of the population Deviation variance 36
LO3-3: Use the Empirical Rule and Chebyshev’s Theorem to describe variation. The Empirical Rule for Normal Populations If a population has mean µ and standard deviation σ and is described by a normal curve, then 68.26% of the population measurements lie within one standard deviation of the mean: [µσ, µ+σ] 95.44% lie within two standard deviations of the mean: [µ2σ, µ+2σ] 99.73% lie within three standard deviations of the mean: [µ3σ, µ+3σ] 37
LO3-3 Chebyshev’s Theorem Let µ and σ be a population’s mean and standard deviation, then for any value k > 1 At least 100(1 1/k2)% of the population measurements lie in the interval [µkσ, µ+kσ] Only practical for nonmoundshaped distribution population that is not very skewed 38
LO3-3 z Scores  For any x in a population or sample, the associated z score is x mean z standard deviation  The z score is the number of standard deviations that x is from the mean ◦ A positive z score is for x above (greater than) the mean ◦ A negative z score is for x below (less than) the mean 39
LO3-4: Compute and interpret percentiles, quartiles, and box-and- whiskers displays. 3.3 Percentiles, Quartiles, and Boxand Whiskers Displays For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements fall at or below the value and (100p) percent of the measurements fall at or above the value  The first quartile Q1 is the 25th percentile  The second quartile (median) is the 50th percentile  The third quartile Q3 is the 75th percentile  The interquartile range IQR is Q3 Q1 310
LO3-5: Compute and interpret covariance, correlation, and the least squares line 3.4 Covariance, Correlation, and the Least Squares Line (Optional) (Optional). When points on a scatter plot seem to fluctuate around a straight line, there is a linear relationship between x and y A measure of the strength of a linear relationship is the covariance sxy n xi x yi y s xy i 1 n 1 311
LO3-6: Compute and interpret weighted means and the mean and standard deviation of grouped data 3.5 Weighted Means and Grouped (Optional). Data (Optional)  Sometimes, some measurements are more important than others ◦ Assign numerical “weights” to the data  Weights measure relative importance of the value  Calculate weighted mean as wi xi wi where wi is the weight assigned to the ith measurement xi 312
LO3-7: Compute and interpret the geometric mean (Optional). 3.6 The Geometric Mean (Optional) For rates of return of an investment, use the geometric mean to give the correct wealth at the end of the investment Suppose the rates of return (expressed as decimal fractions) are R1, R2, …, Rn for periods 1, 2, …, n The mean of all these returns is the calculated as the geometric mean: n Rg 1 R1 1 R2  1 Rn 1 313