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One-Variable Data Analysis 85
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16 Which of the following are properties of the standard deviation Expain your answer a b c d e It s the square root of the average squared deviation from the mean It s resistant to extreme values It s independent of the number of terms in the distribution If you added 25 to every value in the dataset, the standard deviation wouldn t change The interval x 2s contains 50% of the data in the distribution
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17 Look again at the salaries of the Golden State Warriors in question 11 (in millions, 62, 54, 54, 49, 44, 44, 34, 33, 30, 24, 23, 13, 3, 3) Erick Dampier was the highest paid player at \$62 million What sort of raise would he need so that his salary would be an outlier among these salaries 18 Given the histogram below, draw, as best you can, the boxplot for the same data
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19 On the first test of the semester, the class average was 72 with a standard deviation of 6 On the second test, the class average was 65 with a standard deviation of 8 Nathan scored 80 on the first test and 76 on the second Compared to the rest of the class, on which test did Nathan do better 20 What is the mean of a set of data where s = 20, S x = 245, and S (x x )2 = 13 600
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Cumulative Review Problems
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1 Which of the following are examples of quantitative data a b c d e 2 The number of years each of your teachers has taught Classifying a statistic as quantitative or qualitative The length of time spent by the typical teenager watching television in a month The daily amount of money lost by the airlines in the 15 months after the 9/11 attacks The colors of the rainbow
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Which of the following are discrete and which are continuous The weights of a sample of dieters from a weight-loss program The SAT scores for students who have taken the test over the past 10 years The AP Statistics exam scores for the almost 50,000 students who took the exam in 2002 d The number of square miles in each of the 20 largest states e The distance between any two points on the number line a b c
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86 U Step 4 Review the Knowledge You Need to Score High
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3 4 5 Just exactly what is statistics and what are its two main divisions What are the main differences between the goals of a survey and an experiment Why do we need to understand the concept of a random variable in order to do inferential statistics
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Multiple Choice
1 The correct answer is (a) I is correct since the mean is pulled in the direction of the large maximum value, 150 (well, large compared to the rest of the numbers in the set) II is not correct because the mode is y there are three ys and only two 26s III is not correct because 150 is an outlier (you can t actually compute the upper boundary for an outlier since the third quartile is y , but even if you use a larger value, 33, in place of y, 150 is still an outlier) 2 The correct answer is (e) 70 65 z= = 192 percentile = 09726 (see drawing below): 26
(On the TI-83/84, normalcdf ( 100, 192) = normalcdf ( 1000,70,65,206) = 09726 up to rounding error) 3 The correct answer is (d) The effect on the mean of a dataset of subtracting the same value is to reduce the old mean by that amount (that is, mx k = mx k) Because the original mean was 19, and 19 has been subtracted from every term, the new mean is 0 The effect on the standard deviation of a dataset of dividing each term by the same value is to divide the standard deviation by that value, that is,
x =