Exam 3: Numerical Descriptive Measures

The geometric mean is useful in measuring the rate of change of a variable over time.

SCENARIO 3-14-B You are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 100 water bottles to a durability test and the following data on the number of times the handles have been used to lift the bottles before they break are contained in the file Scenario3-14-DataB.XLSX. 493 506 515 491 500 505 517 510 506 503 503 491 495 496 496 505 493 486 504 483 514 494 497 501 493 490 510 494 494 495 494 486 495 506 506 507 502 498 510 501 500 505 492 486 501 496 501 521 510 498 -Referring to Scenario 3-14-B, the coefficient of variation of the number of times the handles have been used to lift the bottles before they break in this sample is ________ percent.

The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.

SCENARIO 3-1 Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 -Referring to Scenario 3-1 determine the third quartile of the ages of the senior citizens.

The line drawn within the box of the boxplot always represents the median.

SCENARIO 3-2 The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings. 11 15 23 29 19 22 21 20 15 25 17 -Referring to Scenario 3-2, the kurtosis statistic for the carbohydrate amount in the cereal is ________.

Which of the following is the easiest to compute?

SCENARIO 3-14-A You are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 100 water bottles to a durability test and the following data on the number of times the handles have been used to lift the bottles before they break are contained in the file Scenario3-14-DataA.XLSX. 495 499 502 500 491 498 498 495 488 516 513 486 504 503 493 504 489 500 495 499 501 507 511 496 486 497 510 504 493 482 511 502 520 514 486 514 500 505 512 500 504 498 503 514 474 489 488 506 517 490 -Referring to Scenario 3-14-A, the coefficient of variation of the number of times the handles have been used to lift the bottles before they break in this sample is ________ percent.

SCENARIO 3-8 The time period from 2010 to 2013 saw a great deal of volatility in the value of stocks. The data in the following table represent the total rate of return of our companies from 2010 to 2013. Year Company A Company B Company C Company D 2013 25.30 26.40 45.40 29.40 2012 -15.01 -22.10 -21.58 -20.90 2011 -5.44 -11.90 -1.03 -10.97 2010 -6.20 -9.10 -3.02 -10.89 -Referring to Scenario 3-8, calculate the geometric mean rate of return per year for Company A.

SCENARIO 3-3 The ordered array below represents the number of vitamin supplements sold by a health food store in a sample of 16 days. 19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41 Note: For this sample, the sum of the values is 448, and the sum of the squared differences between each value and the mean is 812. -Referring to Scenario 3-3, the interquartile range of the number of vitamin supplements sold in this sample is ________.

SCENARIO 3-1 Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 -Referring to Scenario 3-1, calculate the standard deviation of the ages of the senior citizens correct to the nearest hundredth of a year.

According to the Chebyshev rule, at least 75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?

Which of the following is NOT sensitive to extreme values?

SCENARIO 3-14-B You are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 100 water bottles to a durability test and the following data on the number of times the handles have been used to lift the bottles before they break are contained in the file Scenario3-14-DataB.XLSX. 493 506 515 491 500 505 517 510 506 503 503 491 495 496 496 505 493 486 504 483 514 494 497 501 493 490 510 494 494 495 494 486 495 506 506 507 502 498 510 501 500 505 492 486 501 496 501 521 510 498 -Referring to Scenario 3-14-B, the five-number summary of the data in this sample consists of ________, ________, ________, ________, ________.

SCENARIO 3-4 The ordered array below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days: 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 31, 31, 32, 32 Note: For this sample, the sum of the values is 838, and the sum of the squared differences between each value and the mean is 619.89. -Referring to Scenario 3-4, construct a boxplot of this sample.

SCENARIO 3-14-A You are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 100 water bottles to a durability test and the following data on the number of times the handles have been used to lift the bottles before they break are contained in the file Scenario3-14-DataA.XLSX. 495 499 502 500 491 498 498 495 488 516 513 486 504 503 493 504 489 500 495 499 501 507 511 496 486 497 510 504 493 482 511 502 520 514 486 514 500 505 512 500 504 498 503 514 474 489 488 506 517 490 -Referring to Scenario 3-14-A, the average spread around the mean of the number of times the handles have been used to lift the bottles before they break in this sample is ________.

SCENARIO 3-4 The ordered array below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days: 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 31, 31, 32, 32 Note: For this sample, the sum of the values is 838, and the sum of the squared differences between each value and the mean is 619.89. -Referring to Scenario 3-4, the arithmetic mean of the customs data is ________.