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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 ?