ESBE4eAISEsm03 - Chapter 3 Descriptive Statistics:...

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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. 3 - 1 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher.
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Chapter 3 Solutions: 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. 270,377 10,815.08 25 i x x n Σ = Median (Position 13) = 8296 b. Median would be better because of large data values. c. i = (25 / 100) 25 = 6.25 Q 1 (Position 7) = 5984 i = (75 / 100) 25 = 18.75 Q 3 (Position 19) = 14,330 d. i = (85/100) 25 = 21.25 85th percentile (position 22) = 15,593. Approximately 85% of the web sites have less than 15,593 unique visitors. 3 - 2 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher.
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Descriptive Statistics: Numerical Methods 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. Using the mean we get x city =15.58, x country = 18.92 For the samples we see that the mean mileage is better in the country than in the city. City 13.2 14.4 15.2 15.3 15.3 15.3 15.9 16 16.1 16.2 16.2 16.7 16.8 Median Mode: 15.3 Country 17.2 17.4 18.3 18.5 18.6 18.6 18.7 19.0 19.2 19.4 19.4 20.6 21.1 Median Mode: 18.6, 19.4 The median and modal mileages are also better in the country than in the city.
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This note was uploaded on 05/26/2010 for the course ACC 251 taught by Professor Carl during the Winter '09 term at University of Central Arkansas.

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ESBE4eAISEsm03 - Chapter 3 Descriptive Statistics:...

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