Chapter 3 - Practice Problems 2

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1 Chapter 3 - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 1) The grocery expenses for six families were $67.34, $57.68, $50.46, $48.28, $75.94, and $ ) Compute the mean grocery bill. Round your answer to the nearest cent. A) $95.57 B) $76.45 C) $63.71 D) $64.45 Find the median for the given sample data. 2) The salaries of ten randomly selected doctors are shown below. 2) $126,000 $101,000 $195,000 $242,000 $244,000 $144,000 $116,000 $890,000 $241,000 $182,000 Find the median salary. A) $195,000 B) $276,000 C) $248,000 D) $188,500 Find the mode(s) for the given sample data. 3) The speeds (in mi/h) of the cars passing a certain checkpoint are measured by radar. The results are shown below. 3) A) 41.5 mi/hr, 40.1 mi/hr, 44.2 mi/hr B) 41.5 mi/hr C) 44.2 mi/hr D) mi/hr Solve the problem. 4) The amount of money, in dollars, that an employee of a bank spent on lunch on six randomly selected days yielded the following data set. 16, 6, 12, 15, 14, 10 Compute Σ(x - x) 2 4) A) 0 B) C) D) 957 Provide an appropriate response. 5) A study produced the data in the table. x y ) Calculate Σxy. A) 25 B) 43 C) 14 D) 17 1

2 Find the range for the given data. 6) A class of sixth grade students kept accurate records on the amount of time they spent playing video games during a one-week period. The times (in hours) are listed below. 6) A) 8.9 hr B) 8.7 hr C) 19.1 hr D) 14.5 hr Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 7) The manager of a small dry cleaner employs six people. As part of their personnel file, she asked 7) each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below A) 9.00 mi B) mi C) mi D) mi 8) To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: 8) $137 $224 $378 $199 $445 $338 $354 $120 A) $602,253.1 B) $703,415.0 C) $282.5 D) $120.2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 9) We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation? 9) 10) The range and standard deviation of the data set below are 35 and respectively. 10) 5, 24, 25, 26, 40 If the 26 is replaced with 39, how will this affect the range? How will this affect the standard deviation. Use your answers to explain why the standard deviation is preferable to the range as a measure of variation. 2

3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the quartile or interquartile range as specified. 11) The test scores of 19 students are listed below. Find the interquartile range. 11) A) 29 B) 28.5 C) 27 D) 29.5 Obtain the five-number summary for the given data. 12) The normal annual precipitation (in inches) is given below for 21 different U.S. cities. 12) A) 5.1, , 21.30, , 51.7 inches B) 5.1, , 22.6, , 51.7 inches C) 5.1, 14.30, 22.60, 33.80, 51.7 inches D) 5.1, 14.7, 22.6, 32.9, 51.7 inches Construct a boxplot or a modified boxplot as specified. 13) The test scores of 32 students are listed below. Construct a boxplot for the data set. 13) A) B) C) D) 3

4 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 14) Draw one boxplot to illustrate bell-shaped data, another for uniform data, and a third for skewed data. Which of these shapes matches the boxplot for the first 100 digits of π? (Below is the frequency table for the first 100 digits of π.) 14) x f ) Discuss the differences between the distributions represented by the two boxplots below. Explain your reasoning. 15) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 16) Identify potential outliers, if there are any, in the given data. The test scores of 15 students are listed below ) A) 37 B) 99 C) 37, 99 D) None 17) Identify potential outliers, if there are any, in the given data.the ages of the 21 members of a track and field team are listed below ) A) 40, 42 B) 25 C) 15, 42 D) None 4

5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 18) Do men and women run a 5 kilometer race at the same pace? Here are boxplots of the time (in minutes) for a race recently run in Chicago. Explain what the data show. 18) 5

6 Answer Key Testname: CH 3 SET 2 1) C 2) D 3) A 4) B 5) B 6) C 7) A 8) D 9) Answers will vary. Possible answer: The standard deviation will give an indication of how widely the scores vary. More precisely, it gives an indication of how much the scores deviate, on average, from the mean score of ) Answers will vary. Possible answer: The range will be unaffected, while the standard deviation will increase. The standard deviation is preferable as it takes all observations into account while the range depends only on the smallest and largest observations and disregards other observations. 11) A 12) C 13) B 14) Check studentsʹ drawings. The boxplot for a skewed distribution has a long whisker on one side. The boxplots for uniform and bell-shaped distributions are symmetric but for a bell-shaped distribution, the whiskers are long relative to the width of the box. The distribution of the given frequency table is roughly uniform. 15) Answers will vary. Possible answer: The first boxplot represents a bell-shaped distribution since it is symmetrical and has long whiskers relative to the width of the box (indicating that observations close to the mean are more common than those far from the mean). The second boxplot represents a left-skewed distribution, since the whisker to the left is relatively long. 16) A 17) A 18) 6

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