1. Find the median of the following data. Show your work.
84 90 75 65 25 56 78 84 46
2. The mileages of 24 cars were compiled (in miles per gallons):
35 29 37 30 32 44 36 42
26 20 36 19 29 28 20 24
40 27 28 18 41 22 18 37
Summarize the data by constructing a frequency distribution and a relative frequency distribution, using intervals shown below. (Fill in the table provided below.)
|
Mileage (miles per gallon)
|
Frequency
|
Relative Frequency (to the nearest thousandth)
|
|
14.5 - 19.5
|
|
|
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19.5 - 24.5
|
|
|
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24.5 - 29.5
|
|
|
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29.5 - 34.5
|
|
|
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34.5 - 39.5
|
|
|
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39.5 - 44.5
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|
|
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Total
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|
|
3. Consider the following table and pie chart for #3.
Assume that the values in the given table are correct.
Major Number%
| Major |
Number of Seniors |
% of Seniors |
|
Business
|
633
|
33
|
|
Computer Sci.
|
194
|
10
|
|
English 236
|
236
|
12
|
|
Biology 134
|
134
|
7
|
|
Psychology
|
40
|
2
|
|
Other majors
|
681
|
36
|
|
Total Number of Seniors
|
1918
|
100
|
3. Which of the following best describes the most serious problem with the pie chart? (no explanation required)
A. The sizes of the pie wedges are incorrect because the business wedge is too large and the English wedge is too small.
B. The numbers shown in the pie chart for the selected majors do not match the numbers in the % column of the table for those selected majors.
C. The sizes of all the pie wedges are incorrect because an additional wedge must be included.
D. The numbers in the pie chart should be followed by 'to" because the values are percentages.
4. An absent-minded mathematics professor announces that the mean grade on the midterm exam for his class of 10 students is 70. While returning the papers to students, the professor found out that one paper had not been graded and it belonged to the student who had received zero, assuming that he had missed the exam. If the grade on the non-graded midterm exam paper turned out to be 76, what would be the correct class mean to be reported to the class?
NOTE: You should have a good understanding of the meaning of mean and its formula to solve the problem.
5. Choose and write down 10 distinct (different) whole numbers less than 100 in a way that your data set would have a range of 76, a mean of 55, a median of 50, and a mode of your choice. Show your data set and your work to demonstrate that your data set does have the statistical characteristics mentioned.
6. The number of calories per hot dog was determined for 10 brands of poultry hot dogs. The data are
162 102 105 150 135 100 155 100 182
(a) Find the median. Show some work/explanation.
(b) State the mode(s).
(c) Compute the sample mean, the sample variance, and the sample standard deviation.
Use the table below to help organize your work. Fill in the table.
|
xi
|
(xi - x )
|
(xi - x )2
|
|
162
|
|
|
|
102
|
|
|
|
89
|
|
|
|
105
|
|
|
|
150
|
|
|
|
135
|
|
|
|
100
|
|
|
|
155
|
|
|
|
100
|
|
|
|
182
|
|
|
|
Total: Σxi =
|
Total: Σ(xi - x-) =
|
Total: Σ(xi - x-)2 =
|
Mean =
Sample Variance =
Standard Deviation =
(d) What percentage of the data fall within one standard deviation of the mean? Show work/explanation.
7. The probability that an American household has a gun is 0.34. Five American households are selected at random. (Report answers rounded to four decimal places. Show work.)
(a) What is the probability that exactly two of the five households have a gun?
(b) What is the probability that none of the five households has a gun?
(c) What is the probability that at most one of the five households has a gun?
(d) What is the probability that at least one of the five households has a gun?