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name: Mathematics 146 second homework due Tuesday, April 19 , 2016 please show your work to get full credit for each problem 1. A very small population of test scores consists of 5 data values: 100 90 80 70 70 (a) compute the median M and the mean µ of the test scores. (b) compute the M.A.D. (median absolute and the range of the test scores. deviation from the median), the standard deviation σ, (c) what percent of the test scores are within one standard deviation of the mean ? within two standard deviations of the mean ? 2. Suppose a related data set has a very low “outlier” test score: 100 90 80 70 10 Redo parts (a), (b), and (c) of problem one with this new data set to see how much the various measurements of center and dispersion change with the “outlier.” 3. The annual incomes in a certain area are income in $ relative frequency 10, 000, 000 1% 80, 000 9% 40, 000 47% 20, 000 43 % (a) calculate the mode, median, and mean income (b) calculate the standard deviation of the annual incomes (it’s a weighted average !) (c) what percentage of the incomes are within one standard deviation of the mean ? within two standard deviations of the mean ? 4. A university class bases its final class score according to the percentages: 40% final exam score, 30% midterm score, 20% quizzes score, and 10% homework score. If a person wants a 85% final class score, what will they need for a final exam score, given a 75% on the midterm, 74% on the quizzes score, and 88% on the homework score ?