HW #9 (part) – Plots, Percentiles, Measures of Center, and Spread Show all work. 1. Sociology: College Graduates What percentage of the general U.S. population have a bachelor’s degree or higher? The following data set gives the percentage of college graduates for a sample of 25 U.S. states. (Source: The Statistical Abstract of the United States, 129th edition, 2010) 17, 26, 35, 34, 19, 19, 48, 26, 26, 23, 19, 23, 20, 24, 27, 26, 24, 35, 34, 22, 30, 30, 25, 31, 26 a) b) c) d) e) Find the mean, median, and mode. Determine the five number summary. Find the IQR (interquartile range). Draw a box-and-whisker plot. Louisiana has a bachelor’s degree percentage rate of approximately 20% and New Jersey has a bachelor’s degree percentage rate of approximately 34%. Into which quartile does each of those percentage rates fall? f) Are there any potential outliers in this set? Use the IQR method to determine whether or not there any potential outliers. g) Compute a 5% trimmed mean. 2. One standard for admission to Redfield College is that the student rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant? 3. On the NY State Mathematics Assessment, a sixth grader’s score was in the 94 th percentile in their district, but was in the 78th percentile in the state. How does their performance compare to other students in the district and other students in the state? Why might the percentiles be different? 4. 5. Given the population data set: {5, 9, 10, 11, 15} a) Find the mean and standard deviation. b) Add 5 to each data value. Then, find the mean and standard deviation of the new data set. c) Compare the two standard deviation values. In general, how does the standard deviation change when the same constant is added to each data value? Explain. 6. (c)
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