Test Bank For Basic Statistics for Business and Economics 9Th Edition By Douglas Lind

Basic Statistics for Business and Economics, 9e (Lind) Chapter 3 Describing Data: Numerical Measures 1) A value that "attempts to pinpoint the center of a distribution of data" is referred to as a measure of location. Answer: TRUE Explanation: The purpose of a measure of location is to pinpoint the center of a distribution of data. An average is a measure of location that shows the central value of the data. Four measures of location are discussed in the text: the arithmetic mean, the median, the mode, and the geometric mean. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 2) The arithmetic mean is calculated as the sum of the values, divided by the total number of values observed. Answer: TRUE Explanation: This is the formula for calculating the arithmetic mean. It can be used to calculate either population means (for populations) or sample means (for samples). Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 3) For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean. Answer: FALSE Explanation: The median is the midpoint of the values after they have been ordered from the minimum to the maximum values. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 1 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4) A set of ordinal-, interval-, or ratio-level data may have only one mode. Answer: FALSE Explanation: A set of observations may have more than one mode. For example, the following set of data has two modes, 3 and 7: 1, 2, 3, 3, 3, 4, 4, 5, 7, 7, 7, 10. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Reflective Thinking Accessibility: Keyboard Navigation 5) The mode is the value of the observation that appears most frequently. Answer: TRUE Explanation: This is the definition of the mode. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 6) Extremely high or low scores affect the value of the median. Answer: FALSE Explanation: A median is the middle observation in a sorted list of data. High or low values do not have any effect on the median. Arithmetic means are impacted by high or low values, however. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 2 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7) The sum of the deviations of each value (For example: 4, 9, and 5) from the mean of those values, is zero. Answer: TRUE Explanation: This is a basic property of the arithmetic mean, that the sum of deviations away from the mean is zero. The mean of this data set is (4 + 9 + 5)/3 = 6. The deviations from this mean are 4 − 6 = −2, 9 − 6 = +3, and 5 − 6 = −1. The sum of the deviations from the mean are −2 + 3 − 1 = 0. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 8) Ten people are sampled. Three (3) of them earn $8 an hour, six (6) of them earn $9 an hour, and one (1) of them earns $12 an hour. The weighted mean of the hourly wages is $9. Answer: TRUE Explanation: The weighted mean, Difficulty: 2 Medium Topic: The Weighted Mean Learning Objective: 03-02 Compute a weighted mean. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 9) For any set of data, there is an equal number of values above and below the mean. Answer: FALSE Explanation: There is an equal number of observations above and below the median. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 3 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10) The variance is the arithmetic mean of the squared deviations from the median. Answer: FALSE Explanation: The variance is the arithmetic mean of the squared deviations from the mean. Difficulty: 1 Easy Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 11) The standard deviation is the square root of the variance. Answer: TRUE Explanation: The variance must be a positive number as it is based on the squared deviations from the mean. The standard deviation is the square root of the variance. Difficulty: 1 Easy Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 12) For any data set, Chebyshev's theorem estimates the proportion of the values that lie within k standard deviations of the mean, where k is greater than 1.0. Answer: TRUE Explanation: Chebyshev's theorem says that for any set of observations in a population or a sample, the proportion of the values that lie within k standard deviations of the mean is at least 1 − 1/k2, where k > 1. Difficulty: 2 Medium Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 4 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 13) In a company, the standard deviation of the ages of female employees is 6 years and the standard deviation of the ages of male employees is 10 years. These statistics indicate that the dispersion of age is greater for females than for males. Answer: FALSE Explanation: The standard deviation of age for males is larger, indicating there is more dispersion among the males. Difficulty: 2 Medium Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Understand AACSB: Reflective Thinking Accessibility: Keyboard Navigation 14) According to the Empirical rule, about 95% of the observations lie within plus and minus two standard deviations of the mean. Answer: TRUE Explanation: The Empirical rule states that about 95% of observations will lie within two standard deviations above and two standard deviations below the mean. Difficulty: 2 Medium Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 15) The sum of the deviations of each data value from this measure of location will always be zero. A) Mode B) Mean C) Median D) Standard deviation Answer: B Explanation: The sum of the deviations for values less than the mean is equal to the sum of the deviations for values greater than the mean. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 5 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 16) For any data set, which of the following measures of location have only one value? A) Mode and median B) Mode and mean C) Mode and standard deviation D) Mean and median Answer: D Explanation: A set of data can have only one value for the mean and median. A data set can have more than one value for the mode or no mode at all. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 17) Which measures of location are not affected by extremely small or extremely large values? A) Mean and median B) Mean and mode C) Mode and median D) Standard deviation and mean Answer: C Explanation: The mean is affected by large and small values. A median is the middle observation in a sorted list of data. The values do not have any effect on the median. The mode is the value that occurs most frequently. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 6 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 18) What is the relationship among the mean, median, and mode in a symmetric distribution? A) They are all equal. B) The mean is always the smallest value. C) The mean is always the largest value. D) The mode is the largest value. Answer: A Explanation: In a symmetric distribution, the mean, median, and mode are located at the center and are always equal. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 19) For a data set, half of the observations are always greater than the ________. A) median B) mode C) mean D) standard deviation Answer: A Explanation: Half of the observations will be larger than the median and half smaller. This is not necessarily true of the mean and mode. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 20) What is the lowest level of measurement for which a median can be determined? A) Nominal B) Ordinal C) Interval D) Ratio Answer: B Explanation: For the median, the data must be at least an ordinal level of measurement. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 7 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 21) Which of the following mathematical symbols refers to the population mean? A) μ B) s C) σ D) χ Answer: A Explanation: The Greek letter μ identifies the population mean. Generally, Greek letters refer to population parameters. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 22) On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam? A) 89.84 B) 89.33 C) 89.48 D) 10.67 Answer: A Explanation: Multiply the average grade for each of the majors by the number of majors, sum the results, and finally divide the total by 32. [(15 × 90) + (7 × 85) + (10 × 93)]/(15 + 7 + 10) = 89.84. Difficulty: 2 Medium Topic: The Weighted Mean Learning Objective: 03-02 Compute a weighted mean. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 8 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 23) A survey item asked students to indicate their class rank in college: freshman, sophomore, junior, or senior. Which measure(s) of location would be appropriate for the data generated by that questionnaire item? A) Mean and median B) Mean and mode C) Mode and median D) Mode only Answer: C Explanation: Class rank is ordinal scale, so the mode and median are appropriate. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Reflective Thinking Accessibility: Keyboard Navigation 24) What is the median of 26, 30, 24, 32, 32, 31, 27, and 29? A) 32 B) 29 C) 30 D) 29.5 Answer: D Explanation: The observations are first ordered from smallest to largest: 24, 26, 27, 29, 30, 31, 32, 32. Then by convention to obtain a unique value, we calculate the mean of the two middle observations. The two middle observations are 29 and 30. The mean of 29 and 30 is 29.5. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 9 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 25) The net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. What is the mode of the net income? A) $67 B) $85 C) $85.5 D) $86 Answer: D Explanation: The mode is the value of the observation that appears most frequently. The value $86 is the only value that appears more than once. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Communication Accessibility: Keyboard Navigation 26) A stockbroker placed the following order for a customer:  50 shares of Kaiser Aluminum at $104 a share  100 shares of GTE at $25.25 a share  20 shares of Boston Edison at $9.125 a share What is the weighted arithmetic mean price per share? A) $25.25 B) $79.75 C) $103.50 D) $46.51 Answer: D Explanation: Multiply the number of shares by the share price for each stock and sum the results. Divide this result by 170, the total number of shares ordered. [(50 × 104) + (100 × 25.25) + (20 × 9.125)]/(50 + 100 + 20) = 46.51. Difficulty: 3 Hard Topic: The Weighted Mean Learning Objective: 03-02 Compute a weighted mean. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 10 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 27) During the past six months, a purchasing agent placed the following three orders for coal: Tons of Coal 1,200 Price Per Ton $ 28.50 What is the weighted arithmetic mean price per ton? A) $87.25 B) $72.33 C) $68.47 D) $89.18 3,000 500 $ 87.25 $ 88.00 Answer: B Explanation: Multiply the tons of coal purchased by the price per ton and sum the results. Divide this result by 4,700, the total tons purchased. [(1,200 × 28.5) + (3,000 × 87.25) + (500 × 88.00)]/(1,200 + 3,000 + 500) = 72.33. Difficulty: 3 Hard Topic: The Weighted Mean Learning Objective: 03-02 Compute a weighted mean. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 28) A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median? A) 1 B) 2 C) 3 D) 3.5 Answer: C Explanation: Order the six observations from smallest to largest: 699, 826, 839, 880, 965, 1,087. The median is the mean of the two middle observations (839 and 880), or 859.5. There are three observations smaller than this value. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 11 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 29) Over the last six months, the following numbers of absences have been reported: 6, 0, 10, 14, 8, and 0. What is the median number of monthly absences? A) 6 B) 7 C) 8 D) 3 Answer: B Explanation: Order the six observations from smallest to largest: 0, 0, 6, 8, 10, 14. The median value is the mean of the two middle observations (6 and 8). The median is 7. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 30) Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit-hour courses, Statistics a 4 credit- hour course, and Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A, 3 for a B, and 2 for a C, what is the weighted mean grade for the semester? A) 4.00 B) 1.96 C) 2.76 D) 3.01 Answer: C Explanation: Multiply the semester hours per class by the points earned, sum the results, and divide the total by 17, or [(4 × 4) + (5 × 3) + (8 × 2)]/(4 + 5 + 8) = 2.76. Difficulty: 3 Hard Topic: The Weighted Mean Learning Objective: 03-02 Compute a weighted mean. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 12 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 31) A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52, and $55. What is the median charge? A) $47.50 B) $51.00 C) $52.00 D) $55.00 Answer: B Explanation: Order these six observations from smallest to largest: 45, 49, 50, 52, 55, 55. The median value is the mean of the two middle observations (50 and 52). The median is $51.00. Difficulty: 3 Hard Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 32) The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57. What is the median length of time required to review an application? A) 54.5 B) 141.0 C) 97.25 D) 109.0 Answer: A Explanation: Order these four observations from smallest to largest: 50, 52, 57, 230. The median value is the mean of the two middle observations (52 and 57). The median is 54.5. Difficulty: 3 Hard Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 13 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 33) A bottling company offers three kinds of delivery service: instant, same day, and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plant. To find out what effect each type of delivery has on the profit picture, the company summarized the data in the following table based on deliveries for the previous quarter. Type of Delivery Instant Sameday Within five days Frequency per Quarter 100 60 40 Profit per Delivery $ 70 $ 100 $ 160 What is the weighted mean profit per delivery? A) $72 B) $110 C) $142 D) $97 Answer: D Explanation: Multiply the numbers of deliveries by the profit per delivery for each type of service and sum the results. Divide this result ("Total Profits") by 200, the total number of deliveries. The weighted mean profit per delivery is [(100 × 70) + (60 × 100) + (40 × 160)]/[(100 + 60 + 40)] = 97 dollars. Difficulty: 3 Hard Topic: The Weighted Mean Learning Objective: 03-02 Compute a weighted mean. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 14 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 34) For the most recent seven years, the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded? A) About 12,240 B) About 8,327 C) About 6,217 D) About 15,962 Answer: B Explanation: To find the mean, add the degrees earned for each of the seven years and divide the total by 7. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 35) A question in a market survey asks for a respondent's favorite car color. Which measure of location should be used to summarize this question? A) Mode B) Median C) Mean D) Standard deviation Answer: A Explanation: Car color is the nominal scale of measurement. The mode is especially useful in summarizing nominal-level data. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 15 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 36) Sometimes, a data set has two different values that occur with the greatest frequency. In this case, the distribution of the data can best be described as ________. A) symmetric B) bimodal (having two modes) C) positively skewed D) negatively skewed Answer: B Explanation: The distribution is bimodal. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 37) A disadvantage of using an arithmetic mean to summarize a set of data is that ________. A) the arithmetic mean sometimes has two values B) it can be used for interval and ratio data C) it is always different from the median D) it can be biased by one or two extremely small or large values Answer: D Explanation: The mean uses the value of every item in a sample, or population, in its computation. If one or two of these values are either extremely large or extremely small compared to the majority of data, the mean might not be an appropriate average to represent the data. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 16 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 38) The mean, as a measure of location, would be inappropriate for which of the following? A) Ages of adults at a senior citizen center. B) Incomes of lawyers. C) Number of pages in textbooks on statistics. D) Marital status of college students at a university. Answer: D Explanation: Marital status is the nominal scale of measurement. The mean cannot be calculated for nominal scale data. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 39) What is a limitation of the range as a measure of dispersion? A) It is based on only two observations. B) It can be distorted by a large mean. C) It is not in the same units as the original data. D) It has no disadvantage. Answer: A Explanation: If either the largest or smallest value is an extreme value, the range is distorted. Difficulty: 2 Medium Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 17 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 40) The sum of the differences between observations and the mean is equal to ________. A) zero B) the mean deviation C) the range D) the standard deviation Answer: A Explanation: This is one of the properties of the mean. The sum of the negative differences will "balance" the sum of the positive differences and will equal zero. It is why the mean can be considered the balance point of a set of data. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 41) If the variance of the "number of daily parking tickets" issued is 100, the standard deviation is defined as the ________. A) "number of daily parking tickets" B) "number of daily parking tickets" squared C) absolute value of the variance of the "number of daily parking tickets" D) square root of the variance of the "number of daily parking tickets" Answer: D Explanation: The standard deviation is the square root of the variance. So the standard deviation is 10, found by taking the square root of the variance, 100. Difficulty: 2 Medium Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 18 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 42) What is the relationship between the variance and the standard deviation? A) Variance is the square root of the standard deviation. B) Variance is the square of the standard deviation. C) Variance is twice the standard deviation. D) There is no constant relationship between the variance and the standard deviation. Answer: B Explanation: The square root of the variance is the standard deviation. Conversely, if you square the standard deviation you will calculate the variance. Difficulty: 2 Medium Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Understand AACSB: Reflective Thinking Accessibility: Keyboard Navigation 43) According to Chebyshev's theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean? A) 56% B) 95% C) 67% D) 100% Answer: C Explanation: We use Chebyshev's theorem, so 1 − [(1/k2)] = 1 − [1/(1.75)2] = 1 − [1/3.0625] = 1 − .3265 = 0.67 (rounded to two decimal places). Difficulty: 2 Medium Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 19 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 44) For a sample of similar-sized all-electric homes, the March electric bills were (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175, and $194. What is the range? A) $100 B) $130 C) $120 D) $112 Answer: C Explanation: The range is $120, found by the difference between the largest bill ($212) and the smallest ($92). Difficulty: 1 Easy Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Remember AACSB: Analytical Thinking Accessibility: Keyboard Navigation 45) The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range? A) $0 B) $14 C) $52 D) $17 Answer: D Explanation: The range is $17, found by finding the difference between the largest value ($147) and the smallest ($130). Difficulty: 1 Easy Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Remember AACSB: Analytical Thinking Accessibility: Keyboard Navigation 20 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 46) For the past week, a company's common stock closed with the following prices: $61.50, $62.00, $61.25, $60.875, and $61.50. What was the price range? A) $1.250 B) $1.750 C) $1.125 D) $1.875 Answer: C Explanation: The range is $1.125, found by finding the difference between the largest value ($62) and the smallest ($60.875). Difficulty: 1 Easy Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Remember AACSB: Analytical Thinking Accessibility: Keyboard Navigation 47) The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts? A) $100 and $200 B) $85 and $105 C) $205 and $220 D) $110 and $190 Answer: D Explanation: The Empirical rule says that 95% of observations will lie between plus or minus two standard deviations of the mean, or $150 ± 2($20). The lower value is $110 (= $150 − $40) and the upper value is $190 (= $150 + $40). Difficulty: 3 Hard Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 21 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 48) The ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41, and 22. What is the population variance? A) 106.8 B) 91.4 C) 240.3 D) 42.4 Answer: A Explanation: The mean is (38 + 26 + 13 + 41 + 22)/5 = 28. Using formula , Difficulty: 3 Hard Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 49) A sample of assistant professors on the business faculty at state-supported institutions in Ohio revealed the mean income to be $72,000 for nine months, with a standard deviation of $3,000. Using Chebyshev's theorem, what proportion of the faculty earns more than $66,000, but less than $78,000? A) At least 50% B) At least 25% C) At least 75% D) At least 100% Answer: C Explanation: The end values of $66,000 and $78,000 each differ from the mean by $6,000. The value $6,000 is two standard deviations above and below the mean, found by $6,000/$3,000. Using Chebyshev's theorem: 1 − 1/(2)2 = 0.75. Difficulty: 3 Hard Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 22 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 50) A population consists of all the weights of all defensive backs on a university's football team. They are Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)? A) About 4 B) About 16 C) About 100 D) About 40 Answer: A Explanation: The mean is (204 + 215 + 207 + 212 + 214 + 208) / 6 = 210. Using formula , Difficulty: 3 Hard Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 51) A sample of small bottles and their contents has the following weights (in grams): 4, 2, 5, 4, 5, 2, and 6. What is the sample variance of bottle contents weight? A) 6.92 B) 4.80 C) 1.96 D) 2.33 Answer: D Explanation: The sample mean is (4 + 2 + 5 + 4 + 5 + 2 + 6) / (7 − 1) = 4. Using formula , Difficulty: 3 Hard Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Apply AACSB: Analytical Thinking Accessibility: Keyboard Navigation 23 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 52) The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts? A) 13.5 and 14.5 inches B) 13.0 and 15.0 inches C) 13.9 and 14.1 inches D) 13.8 and 14.2 inches Answer: C Explanation: Based on the Empirical rule, 68% of observations are within ±1 standard deviation of the mean. The mean is 14.0 and the standard deviation is 0.1, so the limits are 14.0 ± 0.1. The lower limit is 13.9 inches, and the upper limit is 14.1 inches. Difficulty: 2 Medium Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 53) The sample variance of hourly wages was 10. What is the sample standard deviation? A) $1.96 B) $4.67 C) $3.16 D) $10.00 Answer: C Explanation: The standard deviation is the square root of the variance; the square root of $10 is $3.16. Difficulty: 2 Medium Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 24 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 54) Based on the Empirical rule, what percent of the observations will lie within plus or minus two standard deviations from the mean? A) 95% B) 5% C) 68% D) 2.5% Answer: A Explanation: Based on the Empirical rule, 95% of the observations are within two standard deviations of the mean. Difficulty: 2 Medium Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Understand AACSB: Communication Accessibility: Keyboard Navigation 55) A sample of wires coming off the production line was tested for tensile strength. The statistical results (in PSI) were the following: According to the Empirical rule, 95% of the wires tested had a tensile strength between approximately which of the following two values? A) 450 and 550 B) 460 and 540 C) 420 and 580 D) 380 and 620 Answer: C Explanation: Based on the Empirical rule, 95% of observations are within ±2 standard deviation of the mean. The mean is 500 and the standard deviation is 40, so the limits are 500 ± 80. The lower limit is 420 inches, and the upper limit is 580 inches. Difficulty: 2 Medium Topic: Interpretation and Uses of the Standard Deviation Learning Objective: 03-04 Explain and apply Chebyshevs theorem and the Empirical Rule. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 25 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Arithmetic mean 500Median Mode 500Standard deviation Quartile deviation 25Mean deviation Range 240Sample size 56) Consider two populations with the same mean. Since they have the same mean, then ________. A) their standard deviations must also be the same B) their medians must also be the same C) their modes must also be the same D) None of these is correct. Answer: D Explanation: The mean, median, and mode will only be the same if both populations are perfectly symmetric. Here, we do not know whether the populations are symmetric, only that they have the same mean. Consider two nonsymmetrical populations A and B. Suppose Population A has the following values: 1, 2, 2, 4, 11. The mean of this population is 4, the median is 2, and the mode is 2. Suppose Population B has the following values: 1, 1, 5, 6, 7. The mean of this population is also 4, but the median is 5 and the mode is 1. Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 57) The sample mean ________. A) is always equal to the population mean. B) is always smaller than the population mean. C) is found by adding the data values and dividing them by (n − 1). D) is found by adding all data values and dividing them by n. Answer: D Explanation: The sample mean is found by adding up all data values in the sample and dividing by n, the number in the sample. Sample Mean . Population means are found by adding up all data values in the population and dividing by N, the number in the population. Population Mean . Difficulty: 2 Medium Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Understand AACSB: Analytical Thinking Accessibility: Keyboard Navigation 26 Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 58) The variance of a sample of 121 observations equals 441. The standard deviation of the sample equals ________. A) 11 B) 21 C) 1.91 D) 231 Answer: B Explanation: The standard deviation is the square root of the variance of 441, which is 21. Difficulty: 1 Easy Topic: Why Study Dispersion? Learning Objective: 03-03 Compute and interpret the range, variance, and standard deviation. Bloom's: Remember AACSB: Analytical Thinking Accessibility: Keyboard Navigation 59) When computing the arithmetic mean, the smallest value in the data set ________. A) can never be negative B) can never be zero C) can never be less than the mean D) can be any value Answer: D Explanation: When computing an arithmetic mean, we sum all of the values (in the population or sample) and divide by the number of values. The values can be negative or positive numbers. The smallest value can be any value, but it will be less than the mean unless all the values in the data set are the same. Difficulty: 1 Easy Topic: Measures of Location Learning Objective: 03-01 Compute and interpret the mean, the median, and the mode. Bloom's: Remember AACSB: Analytical Thinking Accessibility: Keyboard Navigation