End Solutions Statistics chapter 3

End Solutions Statistics chapter 3 - Chapter 3 Descriptive...

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Chapter 3 Descriptive Statistics: Numerical Methods 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 = = 5th $134 3 - 2
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Descriptive Statistics: Numerical Methods 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. 6330 422 15 i x x n Σ = = = minutes b. Median 50 15 7.5 100 i = = 8th position 380 minutes c. 85th percentile 85 15 12.75 100 i = = 13th position 690 minutes d. Using the mean x = 422, cell-phone subscribers are using 422/750 = 56% of the capacity of their plans. Part (c) shows 85% of the subscribers are using 690 minutes or less. In general, cell-phone users are not coming close to using the 750 minute capacity of their plans. 7. a. 871.74 36.32 24 i x x n Σ = = = Median is average of 10th and 11th values after arranging in ascending order. 39.00 39.95 Median 39.48 2 + = = Data are multimodal b. 491.14 20.46 24 i x x n Σ = = = 19.75 19.95 Median 19.85 2 + = = Data are bimodal: 19.95 (3 brokers), 29.95 (3 brokers) 3 - 3
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Chapter 3 c. Comparing the measures of central location, we conclude that it costs more to trade 100 shares in a broker assisted trade than 500 shares online. d. From the data we have here it is more related to whether the trade is broker-assisted or online. The amount of the online transaction is 5 times as great but the cost of the transaction is less. However, if the comparison was restricted to broker-assisted or online trades, we would probably find that larger transactions cost more.
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