838 CHAPTER 12 Statistics Section 12.3 Measures of Central Tendency The mean is the sum of the data divided by the number of pieces of data: x x n . = Σ The median is the value in the middle of a set of ranked data. The mode is the piece of data that occurs most frequently (if there is one). The midrange is the value halfway between the lowest and highest values: midrange lowest value highest value 2 . = + Percentiles and quartiles are measures of position. Example 1, page 785 Examples 2–3, 6, pages 786–787 Examples 4, 6, pages 786–787 Examples 5, 6, page 787 Examples 7–8, pages 789-790 Section 12.4 Measures of Dispersion The range is the difference between the highest value and lowest value in a set of data. The standard deviation, s, is a measure of the spread of a set of data about the mean: s x x n ( ) 1 . 2 = Σ − − Discussion, page 798; Example 1, page 798 Examples 2–3, pages 799–801 Section 12.5 z-SCORES z value of the piece of data mean standard deviation = − Discussion, page 809; Examples 1– 4, pages 811–817 Section 12.6 Linear Correlation And Regression Linear correlation coefficient, r, is = Σ − Σ Σ Σ − Σ Σ − Σ r n xy x y n x x n y y ( ) ( )( ) ( ) ( ) ( ) ( ) 2 2 2 2 r is always a value between 1− and 1, inclusive. Equation of the Line of the Best Fit y mx b, = + where = Σ − Σ Σ Σ − Σ = Σ − Σ m n xy x y n x x b y m x n ( ) ( )( ) ( ) ( ) ( ) 2 2 Discussion, pages 823–825; Examples 1–2, pages 825–828 Discussion, pages 828–829; Examples 3– 4, pages 829–831 Review Exercises CHAPTER 12 12.1 1. a) What is a population? A population consists of all items or people of interest. b) What is a sample? A sample is a subset of the population. 2. a) What is a random sample? A random sample is one where every item in the population has the same chance of being selected. b) What is a systematic sample? A systematic sample is obtained by selecting a random starting point and then selecting every nth item in a population.
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