| 20 | ||||||||||
| 1 | The data in a random sample of n = 6 is shown below. Compute the mean and then fill in the deviations column. | |||||||||
| x | Deviation from the mean | |||||||||
| 19 | ||||||||||
| 54 | ||||||||||
| 15 | ||||||||||
| 50 | ||||||||||
| 28 | ||||||||||
| 32 | ||||||||||
| The sum of deviations is. | ||||||||||
| a | 0 | |||||||||
| b | 5 | |||||||||
| c | 10 | |||||||||
| d | 76 | |||||||||
| 2 | In the previous question, the sum of squared deviations is: | |||||||||
| a | 1264 | |||||||||
| b | 1268 | |||||||||
| c | 1272 | |||||||||
| d | 1276 | |||||||||
| 3 | In the previous question, the mean squared deviation for the sample data is: | |||||||||
| a | 250.8 | |||||||||
| b | 255.2 | |||||||||
| c | 258.8 | |||||||||
| d | 262.4 | |||||||||
| 4 | The variance of the data used for the previous three questions is: | |||||||||
| a | 212.7 | |||||||||
| b | 219.2 | |||||||||
| c | 233.7 | |||||||||
| d | 255.2 | |||||||||
| 5 | The mean | |||||||||
| a | balances the number of observations on either side of mean value. | |||||||||
| b | is always the central (or middle) data point. | |||||||||
| c | is the center of gravity of the data. | |||||||||
| d | balances the deviations of the data from the mean. | |||||||||
| e | Both (c) and (d) are correct. | |||||||||
| 6 | The following data is the grade point average (GPA) of five randomly selected E270 students. | |||||||||
| x | ||||||||||
| 3.2 | ||||||||||
| 2.8 | ||||||||||
| 2.5 | ||||||||||
| 3.6 | ||||||||||
| 3.8 | ||||||||||
| The variance of the sample is _______. | ||||||||||
| a | 0.210 | |||||||||
| b | 0.234 | |||||||||
| c | 0.292 | |||||||||
| d | 0.321 | |||||||||
| 7 | Treat the set below as population data: | |||||||||
| x | ||||||||||
| 114 | ||||||||||
| 84 | ||||||||||
| 152 | ||||||||||
| 195 | ||||||||||
| 105 | ||||||||||
| 85 | ||||||||||
| The standard deviation is ________. | ||||||||||
| a | 39.57 | |||||||||
| b | 41.55 | |||||||||
| c | 43.62 | |||||||||
| d | 45.80 | |||||||||
| Tom delivers packages for UPS. His daily mileage for a random sample of 10 days is as follows. | ||||||||||
| x | ||||||||||
| 42 | ||||||||||
| 51 | ||||||||||
| 32 | ||||||||||
| 31 | ||||||||||
| 58 | ||||||||||
| 54 | ||||||||||
| 62 | ||||||||||
| 43 | ||||||||||
| 38 | ||||||||||
| 54 | ||||||||||
| 8 | The average daily miles Tom travels to deliver packages is ______. | |||||||||
| a | 44.5 | |||||||||
| b | 46.5 | |||||||||
| c | 48.5 | |||||||||
| d | 50.5 | |||||||||
| 9 | In the previous question, the sum of squared deviations of daily mileage is ________. | |||||||||
| a | 979.7 | |||||||||
| b | 1010.1 | |||||||||
| c | 1060.5 | |||||||||
| d | 1081.3 | |||||||||
| 10 | Using Tom's daily mileage sample data, on average, Tom's daily mileage deviates from the mean mileage by ________ | |||||||||
| a | 9.12 | miles | ||||||||
| b | 9.86 | miles | ||||||||
| c | 10.03 | miles | ||||||||
| d | 10.86 | miles | ||||||||
| 11 | The following data represents the starting salaries for a sample of 42 students who graduated in 2014 with a bachelor's degree in accounting. Data are in thousands of dollars: | |||||||||
| 53.9 | 54.5 | 59.3 | 60.3 | 63.4 | 64.8 | 58.5 | ||||
| 55.5 | 68.4 | 57 | 68.8 | 62.7 | 50.4 | 48.3 | ||||
| 42 | 63.5 | 61.3 | 57.9 | 45.1 | 62.8 | 45.3 | ||||
| 49.1 | 41.1 | 53.9 | 40.5 | 49.8 | 44.1 | 61.1 | ||||
| 56.9 | 64.5 | 46.6 | 57.1 | 59.3 | 46.7 | 65.8 | ||||
| 67.1 | 40 | 60 | 62.2 | 63.6 | 52.2 | 57.6 | ||||
| Use Excel to expedite your calculations. | ||||||||||
| Find the mean salary (x̅ = ______). Compute the sum of squares of the salary data (∑x² = _______). The numerator of the quotient to compute the variance of the salary data is: _______. | ||||||||||
| a | ∑x² = | 125,620.9 | Numerator of the variance quotient = | 2,775.20 | ||||||
| b | ∑x² = | 128,184.6 | Numerator of the variance quotient = | 2,469.92 | ||||||
| c | ∑x² = | 130,800.6 | Numerator of the variance quotient = | 2,257.56 | ||||||
| d | ∑x² = | 133,470.0 | Numerator of the variance quotient = | 2,775.20 | ||||||
| 12 | The annual salary of the staff in a state government agency are shown below. The first column shows the annual salary and the second column the frequency (the number of staff earning that salary). | |||||||||
| Annual Salary | Frequency | |||||||||
| $102,000 | 1 | |||||||||
| 85,000 | 2 | |||||||||
| 76,000 | 4 | |||||||||
| 50,000 | 10 | |||||||||
| 42,000 | 20 | |||||||||
| 35,000 | 8 | |||||||||
| The mean salary of agency's staff is: | ||||||||||
| a | $48,800 | |||||||||
| b | $55,000 | |||||||||
| c | $63,200 | |||||||||
| d | $65,000 | |||||||||
| 13 | John works in an appliance store. The following is a report of his sales effort in a given month. The report shows the price and the percent of total units sold at that price. What is the mean price of the items sold by John? | |||||||||
| Percent of | ||||||||||
| total units | ||||||||||
| Item | Price | sold | ||||||||
| A | $1,200 | 0.05 | ||||||||
| B | 1000 | 0.20 | ||||||||
| C | 800 | 0.35 | ||||||||
| D | 200 | 0.30 | ||||||||
| E | 50 | 0.10 | ||||||||
| a | x̅ = | $650 | ||||||||
| b | x̅ = | $630 | ||||||||
| c | x̅ = | $615 | ||||||||
| d | x̅ = | $605 | ||||||||
| 14 | The following shows an E270 student’s scores for different course requirements and the corresponding weights assigned by the professor to each category. The scores are from the scale of 100. | |||||||||
| Requirement | Score | Weight | ||||||||
| Homework | 90 | 15% | ||||||||
| Attendance | 100 | 10% | ||||||||
| Tests | 80 | 30% | ||||||||
| Common Final | 70 | 45% | ||||||||
| 100% | ||||||||||
| The student’s mean score is: | ||||||||||
| a | 85 | |||||||||
| b | 84 | |||||||||
| c | 82 | |||||||||
| d | 79 | |||||||||
| The instructor in a Statistics for Business and Economics wants to determine the proportion of students in that class who are business majors. Let "1" stand for business major and "0" for other majors. | ||||||||||
| The following is the distribution obtained from the official class roster. | ||||||||||
| 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | |||
| 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | |||
| 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | |||
| 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | |||
| 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | |||
| 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | |||
| 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | |||
| 15 | The proportion of students who are business majors is ________. | |||||||||
| a | π = | 0.7321 | ||||||||
| b | π = | 0.7143 | ||||||||
| c | π = | 0.6964 | ||||||||
| d | π = | 0.6786 | ||||||||
| 16 | The variance of the above binary data is ________. | |||||||||
| a | 0.1806 | |||||||||
| b | 0.1985 | |||||||||
| c | 0.2181 | |||||||||
| d | 0.2356 | |||||||||
| 17 | A sample data set has n = 50 observations. The mean of the data x̅ = 46.5. The sum of squares ∑x² = 127793. The standard deviation of the data is ______. | |||||||||
| a | 24.25 | |||||||||
| b | 22.05 | |||||||||
| c | 20.04 | |||||||||
| d | 18.04 | |||||||||
| Consider the sample of size 5 with data values of | ||||||||||
| x | ||||||||||
| 16 | ||||||||||
| 12 | ||||||||||
| 20 | ||||||||||
| 10 | ||||||||||
| 17 | ||||||||||
| 18 | Compute the z-scores for each of the five data values. Which of the following is the correct set of z-values? | |||||||||
| a | b | c | d | |||||||
| 0.25 | 0.25 | 0.25 | 0.25 | |||||||
| -0.75 | -0.75 | -0.75 | -0.75 | |||||||
| 1.25 | 1.25 | 1.25 | 0.75 | |||||||
| -1.25 | -1.25 | -0.50 | -0.75 | |||||||
| 0.50 | 0.75 | 1.25 | 0.50 | |||||||
| 19 | The mean of the z-scores in a data set | |||||||||
| a | is always equal to zero | |||||||||
| b | is always equal to one. | |||||||||
| c | is greater than zero for data sets that have large outlying values. | |||||||||
| d | is zero only when the x-values are balanced around the mean of x. | |||||||||
| 20 | The standard deviation of z-scores in a data set | |||||||||
| a | is always equal to zero | |||||||||
| b | is always equal to one. | |||||||||
| c | is one only when the x-values are balanced around the mean of x. | |||||||||
| d | is greater than one for data sets that have large outlying values. | |||||||||
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