AMS 5 Chapter 4: Chapter 4 Review Exercises
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Department
Applied Math and Statistics
Course
AMS 5
Professor
Yonatan Katznelson
Semester
Spring

Description
AMS 5 Practice 4 4/7/2017 (8:00-9:05) Chapter 4, #1, 2, 3, 4, 5, 7, 9, 10, 12 – Math heavy 1. (a) Find the average and SD of the list 41, 48, 50, 50, 54, 57 (b) Which numbers on the list are within .5 SDs of average? Within 1.5 SDs of average? 1a) Average: (41+48+50+50+54+57)/6 = 300/6 = 50 SD: 41-50/ 48-50/ 50-50/ 50-50/ 54-50/ 57-50  -9/ -2/ 0/ 0/ 4/ 7  (81+4+0+0+16+49)/6 = 25^.5 = 5 1b) SD: 5  .5*SD = 2.5; 1.5*SD = 7.5  Avg = 50 Within .5 SDs (47.5-52.5): 3 Within 1.5 SDs (42.5-57.5): 5 2. (a) Both of the following lists have the same average of 50. Which one has the smaller SD, and why? No computations are necessary. (i) 50, 40, 60, 30, 70, 25, 75 (ii) 50, 40, 60, 30, 70, 25, 75, 50, 50, 50, 50 (b) Repeat, for the following two lists. (i) 50, 40, 60, 30, 70, 25, 75 (ii) 50, 40, 60, 30, 70, 25, 75, 99, 1 2a) (ii), since it has more elements and thus a larger denominator before the final square root. 2b) (i), since the outliers (99, 1) increase the numerator of the fraction before the final square root and make the final answer much larger. 3. Here is a list of numbers: 0.7 1.6 9.8 3.2 5.4 0.8 7.7 6.3 2.2 4.1 8.1 6.5 3.7 0.6 6.9 9.9 8.8 3.1 5.7 9.1 (a) Without doing any arithmetic, guess whether the average is around 1, 5, or 10. (b) Without doing any arithmetic, guess whether the SD is around 1, 3, or 6. 3a) 5 Math: (.7+6.3+1.6+5.4+9.8+3.2+7.7+2.2+4.1+.8+8.1+9.9+6.5+.3+3.1+9.1+3.7+.3+6.9+8.8+5.7)/10 = (13+7+7+14+.8+18+19+4+21.4)/20 = 2.09 + 3.12 = 5.21 3b) 3 Math: …how about no? I do this all mentally, mind you. 4. For persons age 25 and over in the U.S., would the average or the median be higher for income? For years of schooling completed? 4) Average (Most people fall on the lower end, however those on the high end earn a mind- boggling amount and raise the average way up); Median (since typically you go through more school for more technical and higher-paying jobs and most people don’t go to college) 5. For the men age 18-24 in HANES5, the average systolic blood pressure was 116 mm and the SD was 11 mm. Say whether each of the following blood pressures is unusually high, unusually low, or about average: 80 mm 115 mm 120 mm 210 mm 5) (Low <= 105 mm < Average < 127 mm <= High) Low; Average; Average; High 7. A study on college students found that the men had an average weight of about 66 kg and
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