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Name ______________________________________________ Date _______________________________________ Algebra II & Trigonometry Measures of Dispersion A2.S.3 A2.S.4 Calculate measures of central tendency with group frequency distributions Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations 1. If the range of a set of data is 40 and the highest score is 50, what is the lowest score? (1) –10 (3) 10 (2) 1.2 (4) 90 2. If the variance of a set of data is 16, what is the standard deviation? (1) 256 (3) 8 (2) 32 (4) 4 3. If the standard deviation of a set of data is 16, what is the variance? (1) 256 (3) 8 (2) 32 (4) 4 4. Which of the following sets of data has the greatest range? (1) {32, 65, 34, 43, 16} (2) {14, 76, 56, 42, 86} (3) {65, 54, 75, 45, 86} (4) {21, 45, 90, 65, 54} 5. What is the variance for the following set of data: 4, 6, 8, 10, 12 (1) 1.682 (2) 2.828 (3) 8 (4) 64 6. What is the interquartile range of the following set of data: 22, 48, 18, 34, 59, 47, 16, 82, 11, 39 Show how you arrived at your result. 7. After giving a test to her class, Mrs. Statsrule decided to raise everyone’s score by 5 points. How does this affect the standard deviation? (1) increases it by 5 points (2) increased it by 5 points (3) there is no change (4) the change cannot be determined 8. What is the sample standard deviation for the following set of data: (1) 6.9 (2) 7.6 (3) 16.8 (4) 101 6, 12, 14, 19, 24, 26 9. What is the population standard deviation for the following set of data? 6, 12, 14, 19, 24, 26 (1) 6.9 (2) 7.6 (3) 16.8 (4) 101 10. The table below shows the temperature in various places in New York State on July 22, 2008. Location Temperature Location Albany 85 New York City Binghamton 81 Niagara Falls Buffalo 77 Oswego Corning 81 Plattsburg Dunkirk 75 Poughkeepsie Elmira 81 Rochester Geneva 79 Saranac lake Glens Falls 81 Syracuse Islip 85 Utica Ithaca 81 Watertown Kingston 85 White Plains Massena 79 Yonkers Temperature 89 77 77 80 85 79 75 81 81 77 89 89 (a) According to the data, to the nearest tenth, what was the mean temperature in New York State on July 22, 2008? (b) If we use standard deviation as a measure of dispersion, would we find sample standard deviation or population standard deviation in this case? Explain. (c) What is the appropriate standard deviation of the temperatures, to the nearest tenth? 11. Both of the following sets of data have the same mean. Without doing any computation, determine which one has the smaller standard deviation. Explain how you came to your conclusion. A: 10, 90, 40, 5, 30, 5 B: 32, 30, 36, 28, 24, 30 12. The PSAT scores of a group of students in Kennedy High School are given in the table below. Score Frequency Score Frequency Score 20 1 45 28 70 25 2 50 36 75 30 2 55 34 80 35 2 60 27 40 14 65 23 Frequency 11 3 2 (a) Based on the data given above, to the nearest hundredth, what is the mean PSAT score of these students? (b) To the nearest hundredth, what is the sample standard deviation of the students in Kennedy High School? 13. The name, year of birth, and year of appointment for the 2008 Supreme Court justices are listed in the table below. Name John G. Roberts (Chief Justice) Samuel A. Alito, Jr. Stephen Breyer Ruth Bader Ginsburg Anthony M. Kennedy Antonin Scalia David Souter John Paul Stevens Clarence Thomas Year of Birth 1955 1950 1938 1933 1936 1936 1939 1920 1948 Year of Appointment 2005 2006 1994 1993 1988 1986 1990 1975 1991 (a) Find, to the nearest tenth, the mean, median, and first and third quartiles of the number of years the Supreme Court justices have served as of 2008. (b) Find the range of their years of service and the interquartile range of their years of service as of 2008. (c) What is the “average” age of a Supreme Court justice as of 2008? Explain why you chose the measure of central tendency that you did. 14. The table below lists the ages of people who attended the Screaming Ghouls rock concert. Age 12 13 14 15 16 17 18 Frequency 23 46 56 65 43 38 21 Age 19 20 21 22 23 31 42 (a) What is the mean age of the rock concert attendees, to the nearest hundredth? (b) What is the standard deviation, to the nearest hundredth? (c) Who would be interested in this type of information? Frequency 11 10 6 3 2 2 1