**Place all work on a separate sheet of paper. Do not turn in this sheet.**
Neatness and format count in all work. All work you turn in must be your own. Any work that involves copying will result in a grade of 0 for the entire assignment for all parties involved, regardless of who did the original work and how much of the assignments is involved.
**Point value are in parenthesis**
All tables and graphs must be appropriately labeled. All answers must contain appropriate units to be complete.
1. The following data represent trunk circumferences (in mm) for a random sample of 59 four-year old apple trees.
108 99 106 102 115 120 117 122 142 106 111 119 109 125 108 116 105 117 123 103 114 101 99 112 120 108 91 115 109 114 105 99 122 106 113 114 75 96 124 91 102 108 110 83 90 69 117 84 142 122 113 105 112 117 122 129 100 138 117
a) Make a frequency table with 8 classes showing class limits and class frequencies. (7)
b) Make a list of all class boundaries and class midpoints for your table. (6)
c) Draw a histogram. How would you describe the distribution of the data? (8)
d) Make a stem and leaf plot (7)
2. Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researched conducted a study of lawsuits involving 1908 business ranked in the Fortune 1000 over a 20-year period. They found the following distribution of civil justice cases brought before the federal courts involving businesses:
Case Type Number of Filings (in thousands)
Contracts 107
Personal Injury 191
Asbestos liability 49
Other product liability 38
All other 21
a) Make a pareto chart. (7)
b) Make a pie chart, clearly show all calculations of degrees for each sector. (7)
3. The circumferences of 94 blue spruce trees selected at random in Roosevelt National Forest were measured. The results to the nearest inch were recorded in the table below.
Circumference (inches) Number of Trees
10-24 6
25-39 20
40-54 52
55-69 16
Find the mean and the standard deviation for such trees. (8) Use the method of your choice.
4. A certain brand of nylon fishing line is known to deteriorate in very cold temperatures. A spool of such line was left out overnight in Fairbanks, Alaska, when temperatures dropped to -35oF. A random sample of six pieces of line gave the following breaking strengths (in pounds):
10.1 6.2 9.8 5.3 9.9 5.7
A second spool that has not been subjected to extreme cold, yielded the following breaking strengths (in pounds) for six pieces of line:
10.2 9.7 9.8 10.3 9.6 10.1
a) Compute the mean and range for each of the samples. (8)
b) Compute the standard deviation for sample 1 using the formula we used in class. (6)
c) Compute the standard deviation for the second sample using the method of your choice. (By hand or by calculator.) (4)
d) Compare your answers in part a and comment on the observed differences. Which line had a more consistent performance? How was this reflected in the standard deviations? Does this evidence seem to show that the lines deteriorate in cold temperatures? Explain all of your answers and conclusions in full sentences. (10)