Exam 3: Numerical Descriptive Measures

According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?

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 D.

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, what type of shape does the distribution of the sample appear to have?

SCENARIO 3-7 In a recent academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the previous academic year for a sample of 10 public universities were as follows: $1,589, $593, $1,223, $869, $423, $1,720, $708, $1425, $922 and $308. -Referring to Scenario 3-7, what is the standard deviation of the change in the cost?

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 variance of the ages of the senior citizens correct to the nearest hundredth of a year squared.

The coefficient of variation is expressed as a percentage.

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, half of the bottles in this sample have a broken handle after being used to lift the bottles for less than how many times?

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, is the number of times the handles have been used to lift the bottles before they break in this sample lepokurtic or platykurtic?

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 interquartile range of the number of times the handles have been used to lift the bottles before they break in this sample is ________.

The interquartile range is a measure of central tendency in a set of data.

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, is the carbohydrate amount in the cereal right- or left-skewed?

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 1 standard deviation around the arithmetic Mean.

SCENARIO 3-12 Given below are the rating and performance scores of 15 laptop computers. Performance Score 115 191 153 194 236 184 184 216 Overall Rating 74 78 79 80 84 76 77 92 Performance Score 185 183 189 202 192 141 187 Overall Rating 83 78 77 78 78 73 77 -Referring to Scenario 3-12, you will expect a decrease in the performance score of one laptop computer to be associated with

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, is the number of vitamin supplements sold in this sample right- or left- skewed?

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 first quartile of the number of times the handles have been used to lift the bottles before they break in this sample is ________.

SCENARIO 3-7 In a recent academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the previous academic year for a sample of 10 public universities were as follows: $1,589, $593, $1,223, $869, $423, $1,720, $708, $1425, $922 and $308. -Referring to Scenario 3-7, what is the interquartile range of the change in the cost?

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 arithmetic mean age of the senior citizens to the nearest hundredth of a year.

The five-number summary consists of the smallest value, the first quartile, the median, the third quartile, and the largest value.

When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate:

A boxplot is a graphical representation of a five-number summary.