1. Find the median of the following data. Show work.
86 92 80 66 27 59 76 86 48
2. The mileages of 24 cars were compiled (in miles per gallons):
24 20 28 29 19 36 20 26
37 18 22 41 18 28 27 40
42 36 44 32 30 37 29 35
Summarize the data by constructing a frequency distribution and a relative frequency distribution, using intervals shown below. (Fill in the table.)
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Mileage(miles per gallon)
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Frequency
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Relative Frequency (to the nearest thousandth)
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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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Total
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3. Consider the following table and pie graph (pie chart) before answering the question. Assume that the values in the given table are correct.
Major Number of Seniors % of Seniors
Business 633 33
Computer Sci. 194 10
English 236 12
Biology 134 7
Psychology 40 2
Other majors 681 36
Total Number of Seniors 1918 100
Which of the following best describes the most serious problem with the pie chart?
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 "%" because the values are percentages.
4. The number of calories per hot dog was determined for 10 brands of poultry hot dogs. The data are
184 102 157 102 137 152 107 91 104 164
(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.
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xi
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(xi - x-)
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(xi - x-)2
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184
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102
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157
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102
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137
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152
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107
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91
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104
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164
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Total:
Σxi =____
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Total:
Σ(xi - x-) =_____
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Total:
Σ(xi - x-)2 =______
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Mean = _____________
Sample Variance = ________________
Standard Deviation= _______________
(d) What percentage of the data fall within one standard deviation of the mean? Show work/explanation.
5. Exam scores.Find the mean for the grouped data in the following table. Report the mean to the nearest tenth. Show work.(Extra space provided in table for scratch work.)
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40 Exam Scores
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Interval
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Frequency
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49.5 - 59.5
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3
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59.5 - 69.5
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7
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69.5 - 79.5
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9
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79.5 - 89.5
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13
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89.5 - 99.5
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8
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6. At a university, the probability that a student brings a laptop computer (laptop) to classes is0.66.Sixstudents from that university are selected at random. (Report answers rounded to four decimal places. Show work.)
(a) What is the probability that none of the six students brings a laptop to classes?
(b) What is the probability that all six of the students bring laptops to classes?
(c) What is the probability that at most one of the six students brings a laptop to classes?