# Chap 3 - Chapter 3 Descriptive Statistics Numerical...

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Chapter 3 Descriptive Statistics: Numerical Measures Learning Objectives 1. Understand the purpose of measures of location. 2. Be able to compute the mean, median, mode, quartiles, and various percentiles. 3. Understand the purpose of measures of variability. 4. Be able to compute the range, interquartile range, variance, standard deviation, and coefficient of variation. 5. Understand skewness as a measure of the shape of a data distribution. Learn how to recognize when a data distribution is negatively skewed, roughly symmetric, and positively skewed. 6. Understand how z scores are computed and how they are used as a measure of relative location of a data value. 7. Know how Chebyshev’s theorem and the empirical rule can be used to determine the percentage of the data within a specified number of standard deviations from the mean. 8. Learn how to construct a 5-number summary and a box plot. 9. Be able to compute and interpret covariance and correlation as measures of association between two variables. 10. Be able to compute a weighted mean. Solutions: 3 - 1

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Chapter 3 1. x x n i = = = Σ 75 5 15 10, 12, 16, 17, 20 Median = 16 (middle value) 2. x x n i = = = Σ 96 6 16 10, 12, 16, 17, 20, 21 Median = 16 17 16.5 2 + = 3. 15, 20, 25, 25, 27, 28, 30, 34 20 (8) 1.6 100 i = = 2nd position = 20 25 (8) 2 100 i = = 20 25 22.5 2 + = 65 (8) 5.2 100 i = = 6th position = 28 75 (8) 6 100 i = = 28 30 29 2 + = 4. Mean = = = Σ x n i 657 11 59 727 . Median = 57 6th item Mode = 53 It appears 3 times 5. a. 3181 \$159 20 i x x n Σ = = = b. Median 10th \$160 Los Angeles 11th \$162 Seattle Median = 160 162 \$161 2 + = c. Mode = \$167 San Francisco and New Orleans d. 25 20 5 100 i = = 3 - 2
Descriptive Statistics: Numerical Measures 5th \$134 6th \$139 1 134 139 \$136.50 2 Q + = = e. 75 20 15 100 i = = 15th \$167 16th \$173 3 167 173 \$170 2 Q + = = 6. a. Marketing Majors 363 36.3 10 i x x n Σ = = = Data in order 28.4 30.6 34.2 34.2 35.2 35.8 37.7 39.5 42.4 45.0 Median (5 th and 6 th ) = 35.2 35.8 35.5 2 + = Mode – 34.2 (2 times) Accounting Majors 731.2 45.7 16 i x x n Σ = = = Data in order 33.5 38.0 40.2 40.8 41.1 41.7 43.5 44.2 45.2 47.8 49.1 49.7 49.9 53.9 55.5 57.1 Median (8 th and 9 th ) = 44.2 45.2 44.7 2 + = There is no mode – all values occur one time. b. Marketing Q 1 : i = .25(10) = 2.5 Round to 3 rd position Q 1 = 34.2 Q 3 : i = .75(10) = 7.5 Round to 8 th position Q 3 = 39.5 Accounting 3 - 3

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Chapter 3 Q 1 : i = .25(16) = 4 Use 4 th and 5 th positions Q 1 = 40.8 41.1 40.95 2 + = Q 3 : i = .75(16) = 12 Use 12 th and 13 th positions Q 3 = 49.7 49.9 49.8 2 + = c. The difference between the sample means is 45.7 – 36.3 = 9.4. The difference between the sample medians is 44.7 – 35.5 = 9.2. On the basis of both of these measures of central location, accounting majors have an average salary that is slightly over \$9,000 more per year than marketing majors. The highest accounting major salary was \$57,1000, while the highest marketing major salary was
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Chap 3 - Chapter 3 Descriptive Statistics Numerical...

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