Instructions: Use the data set representing a sample in Table 4 to answer the questions ( Note: Review the 1-Var Stats function on the TI83/84 calculator; Avoid doing these calculations by hand.).
| Table 4. Data for problems 8-11. | ||||
| Sample Data | ||||
| 48 | 53 | 96 | 76 | 81 |
| 66 | 108 | 84 | 30 | 92 |
| 62 | 47 | 91 | 83 | 120 |
| 50 | 99 | 122 | 75 | 58 |
8. What is the range?
9. What is the mean?
10. What is the variance?
11. What is the standard deviation?
Problems 12-14.
InstructionsUse the data sets in tables 5A and 5B below to answer answer the questions.
| Table 5A. Data set A | |||||||||
| Data set A | |||||||||
| 4.2 | 3.8 | 5.8 | 5.3 | 7.4 | 3.5 | 6.2 | 7.5 | 4.9 | 3.9 |
| Table 5B. Data set B | |||||||||
| Data set B | |||||||||
| 10.0 | 2.0 | 8.1 | 7.5 | 0 | 2.8 | 8.6 | 9.0 | 0.2 | 0.7 |
12. Select the letter of the appropriate data set for your answer. Without calculating the standard deviation, which data set has the least standard deviation?
13. Select the letter of the appropriate data set for your answer. Without calculating the standard deviation, which data set has the greatest standard deviation?
14. Explain the reason for your decisions in questions 12 and 13.
15. Salary Offers. You are applying for a job at two companies. Company A offers salaries with μ=$46,000μ=$46,000 and σ=$2,500σ=$2,500 and company B offers salaries with μ=$46,000μ=$46,000 and σ=$5000σ=$5000. Which company is most likely to offer a starting salary of $61,000 or more?
16. Use the empirical rule to solve the problem. The mean value of land and buildings per acre from a sample of farms is $7800, with a standard deviation of $602. Between what two values do about 95% of the data lie?
Problems 17-19
Instructions Use the following information and Table 6 to answer the questions.
Coefficient of variation. The coefficient of variation (CV) is an alternate way to measure variation. The CV expresses the standard deviation as a percent of the mean. Because it has no unit of measure, you can use the coefficient of variation to compare the variability of data with different units of measure. Note: Either the sample standard deviation, ss, or the population standard deviation, σσ, may be used for calculating the CV. Use the appropriate value of the standard deviation depending on whether the data pertain to a population or a sample.
CV=standard deviationMean×100%
| Table 6. Line voltage at a computer. | ||||||||
| Protection | Line voltage (volts) | |||||||
| No Surge Protector | 73 | 140 | 78 | 142 | 80 | 140 | 90 | 133 |
| With Surge Protector | 100 | 120 | 108 | 114 | 105 | 117 | 103 | 114 |
17. Find the coefficient of variation for the voltages with no surge protector (Round your answer to 3 decimal places).
18. Find the coefficient of variation for the voltages with a surge protector (Round your answer to 3 decimal places).
19. What do you conclude from the results in questions 17 and 18?.
Section 2.5
20. True or False? If a data set has Q1=14, Q2=15, and Q3=16, then a data value of 10 would be considered an outlier.
21. True or False? 75% of the data in a data set with quantitative data is between Q1 and Q3.
Problems 22-25
Instructions Use the data in Table 7 to answer the questions.
| Table 7. Dataset for problems 23-25 | ||||||||
| Data | ||||||||
| 94.1 | 122.4 | 101.9 | 105.1 | 80.9 | 118.9 | 90.1 | 96.9 | 108.2 |
| 78.4 | 94.0 | 105.2 | 106.7 | 83.9 | 85.6 | 117.2 | 112.1 | 94.8 |
| 78.2 | 96.6 | 104.9 | 113.7 | 72.3 | 108.4 | 102.6 |
22. What is Q1Q1?
23. What is Q2Q2?
24. What is Q3Q3?
25. Draw a box-and-whisker plot that represents the data set in Table 7. ( Note: When drawing the box-and-whisker plot, please label the 5-number summary values. If you are doing a hand sketch, select an appropriate scale, and use graph paper.)
