MATH 201Review for Exam 1 PRACTICE EXAM QUESTIONS AND ANSWERS 100%

MATH 201Review for Exam 1 PRACTICE EXAM QUESTIONS AND ANSWERS 100% 1. Determine if the statement is true or false. If it is false, rewrite it as a true statement. It is impossible for the Census Bureau to obtain all the census data about the population of the United States. Choose the correct answer below. A. The statement is true. B. The statement is false. It is possible for the Census Bureau to obtain all the census data about the population of the United States. C. The statement is false. It is possible for the Census Bureau to obtain all the census data about the population of some states. 2. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A population is the collection of some outcomes, responses, measurements, or counts that are of interest. Choose the correct answer below. A. True. B. False. A sample is the collection of all outcomes, responses, measurements, or counts that are of interest. C. False. A population is the collection of all outcomes, responses, measurements, or counts that are of interest. 3. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A population is the collection of some outcomes, responses, measurements, or counts that are of interest. Choose the correct answer below. A. False. A population is the collection of all outcomes, responses, measurements, or counts that are of interest. B. False. A sample is the collection of all outcomes, responses, measurements, or counts that are of interest. C. True. 4. Determine whether the data set is a population or a sample. Explain your reasoning. The number of garages for each house on a street. Choose the correct answer below. A. Sample, because it is a collection of the number of garages for some houses on the street. B. Sample, because it is a collection of the number of garages for all houses on the street, but there are other houses on different streets. C. Population, because it is a collection of the number of garages for all houses on the street. D. Population, because it is a subset of all houses in the town. 5. Determine whether the data set is a population or a sample. Explain your reasoning. The number of garages for each house on a street. Choose the correct answer below. A. Sample, because it is a collection of the number of garages for all houses on the street, but there are other houses on different streets. B. Sample, because it is a collection of the number of garages for some houses on the street. C. Population, because it is a subset of all houses in the town. D. Population, because it is a collection of the number of garages for all houses on the street. 6. A polling organization contacts 2656 undergraduates who attend a university and live in the United States and asks whether or not they had spent more than $200 on food in the last month. What is the population in the study? A. Undergraduates who attend a university. B. Undergraduates who attend a university and have spent more than $200 on food. C. Undergraduates who attend a university and live in the United States. D. Undergraduates who attend a university and live in the United States and have spent more than $200 on food. What is the sample in the study? A. Undergraduates who attend a university. B. Undergraduates who attend a university and live in the United States. C. The 2656 undergraduates who attend a university and have spent more than $200 on food. D. The 2656 undergraduates who attend a university and live in the United States. 7. A quality-control manager randomly selects 50 bottles of tomato sauce that were filled on January 23 to assess the calibration of the filling machine. What is the population in the study? A. The 50 bottles of tomato sauce selected in the plant on January 23. B. The 50 bottles of tomato sauce selected in the plant. C. Bottles of tomato sauce produced in the plant. D. Bottles of tomato sauce produced in the plant on January 23. What is the sample in the study? A. The 50 bottles of tomato sauce selected in the plant on January 23. B. Bottles of tomato sauce produced in the plant on January 23. C. Bottles of tomato sauce produced in the plant. D. The 50 bottles of tomato sauce selected in the plant in January. 8. Determine whether the given value is a statistic or a parameter. In a study of all 2358 seniors at a college, it is found that 65% own a computer. Choose the correct statement below. Statistic because the value is a numerical measurement describing a characteristic of a sample. Statistic because the value is a numerical measurement describing a characteristic of a population. Parameter because the value is a numerical measurement describing a characteristic of a sample. Parameter because the value is a numerical measurement describing a characteristic of a population. 9. Determine whether the given value is a statistic or a parameter. In a study of all 1715 students at a college, it is found that 40% own a computer. Choose the correct statement below. Statistic because the value is a numerical measurement describing a characteristic of a population. Statistic because the value is a numerical measurement describing a characteristic of a sample. Parameter because the value is a numerical measurement describing a characteristic of a population. Parameter because the value is a numerical measurement describing a characteristic of a sample. 10. Suppose that a study based on a sample from a targeted population shows that people who drink sports drinks regularly are in better shape than those who do not. (a) Make an inference based on the results of this study. (b) What might this inference incorrectly imply? (a) Make an inference based on the results of the study. Choose the correct answer below. A. People who do not drink sports drinks are in better shape than those who do. B. People who drink sports drinks on a regular basis also exercise regularly. C. People who play sports drink sports drinks regularly. D. People who drink sports drinks regularly are in better shape than those who do not drink sports drinks regularly. (b) What might this inference incorrectly imply? A. This inference may incorrectly imply that if you drink sports drinks regularly, you will be in better shape than if you do not. B. This inference may incorrectly imply that people who drink sports drinks on a regular basis also exercise regularly. C. This inference may incorrectly imply that people who play sports drink sports drinks regularly. D. This inference may incorrectly imply that if you do not drink sports drinks regularly, you will be in better shape than if you do. 11. A study shows that the obesity rate among boys ages 2 to 19 has increased over the past several years. Complete parts a and b. (a) Make an inference based on the results of this study. Choose the correct answer below. A. The obesity rate is increasing. B. The obesity rate among boys is increasing. C. The obesity rate among boys ages 2 to 19 is increasing. (b) What is wrong with this type of reasoning? Choose the correct answer below. A. This inference may incorrectly imply that the trend will continue in future years. B. An inference cannot be drawn from only a single study. C. Inferences cannot be drawn because the sample size was not large enough. 12. Name each level of measurement for which data can be qualitative. Select all the levels of measurement for which data can be qualitative. A. Ordinal B. Nominal C. Ratio D. Interval 13. Determine whether the variable is qualitative or quantitative. Explain your reasoning. Country of residence Is the variable qualitative or quantitative? A. The variable is qualitative because country of residence is found by measuring or counting. B. The variable is qualitative because country of residence describes an attribute or characteristic. C. The variable is quantitative because country of residence is found by measuring or counting. D. The variable is quantitative because country of residence describes an attribute or characteristic. 14. Determine whether the variable is qualitative or quantitative. Explain your reasoning. Amount of disk space in gigabytes Is the variable qualitative or quantitative? A. The variable is quantitative because amount of disk space describes an attribute or characteristic. B. The variable is quantitative because amount of disk space is found by measuring or counting. C. The variable is qualitative because amount of disk space describes an attribute or characteristic. D. The variable is qualitative because amount of disk space is found by measuring or counting. 15. The graph to the right shows the number of cities with certain average annual rainfall amounts (in inches). Identify the level of measurement of the data listed on the horizontal and vertical axes in the figure. 50 40 30 20 10 0 A B C D E A: 1 B: 2 C: 3 D: 4 E: 5 Number of cities Identify the level of measurement of the data listed on the horizontal axis in the figure. Choose the correct answer below. Ratio Interval Nominal Ordinal Identify the level of measurement of the data listed on the vertical axis in the figure. Choose the correct answer below. Nominal Interval Ratio Ordinal 16. The following appear on a physician's intake form. Identify the level of measurement of the data. (a) Year of birth (b) Weight (c) Allergies (d) Pain level (scale of 0 to 10) (a) What is the level of measurement for "Year of birth"? Ratio Interval Nominal Ordinal (b) What is the level of measurement for "Weight"? Ordinal Ratio Interval Nominal (c) What is the level of measurement for "Allergies"? Interval Nominal Ordinal Ratio (d) What is the level of measurement for "Pain level (scale of 0 to 10)"? Nominal Ratio Interval Ordinal 17. What is an inherent zero? Describe three examples of data sets that have inherent zeros and three that do not. Choose the correct answer below. A. An inherent zero is a value that the variable can take. B. An inherent zero is a zero that implies none. C. An inherent zero is a zero that occurs in the data set naturally. Select three examples of data sets that have inherent zeros below. A. Maximum wind speed during a hurricane B. Average IQ score of a high school class C. Average age of college students in years D. Temperature in degrees Fahrenheit E. A student's level of happiness measured from 0 to 10 F. Average monthly percipitation in inches Select three examples of data sets that do not have inherent zeros below. A. Temperature in degrees Fahrenheit B. A student's level of happiness measured from 0 to 10 C. Average IQ score of a high school class D. Average monthly percipitation in inches E. Maximum wind speed during a hurricane F. Average age of college students in years 18. What is the difference between a random sample and a simple random sample? Choose the correct answer below. A. With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected. B. With a random sample, all samples of the same size have the same chance of being selected. With a simple random sample, each individual has the same chance of being selected. 19. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Using a systematic sample guarantees that members of each group within a population will be sampled. Choose the correct answer below. A. False. Using a stratified sample guarantees that members of each group within a population will be sampled. B. True. C. False. Using a cluster sample guarantees that members of each group within a population will be sampled. 20. A researcher wants to study the effects of sleep deprivation on motor skills. Nine people volunteer for the experiment: Amanda, Brian, Christine, David, Emily, Fred, George, Heather, and Ivan. Use the second row of digits in the random number table below to select a simple random sample of three subjects (ignore zeros). The other six subjects will go into the control group. If the subjects are numbered 1 through 9 alphabetically, what are the numbers of the three subjects selected? List the subjects that will go in the treatment group. Line/Column (1) (2) (3) (4) 1 37330 87385 32323 71009 2 46254 15935 65321 89215 3 65216 32341 68693 55931 What are the numbers of the three subjects selected? , , The three subjects, in the order selected, are (1) (2) and (3) (1) Brian, David, Christine, Ivan, (3) Fred. Christine. David. Amanda. Amanda, Emily, Fred, George, Emily. Brian. Ivan. Heather. Heather, (2) Emily, David, Christine, Brian, George. George, Heather, Fred, Amanda, Ivan, 21. Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. In 1965, researchers used random digit dialing to call 1200 people and ask what obstacles kept them from buying insurance. What type of sampling was used? A. Convenience sampling was used, since the 1200 phone numbers that were easiest to reach were selected. B. Cluster sampling was used, since the phone numbers were divided into groups, several groups were selected, and each number in those groups was called. C. Simple random sampling was used, since each number had an equal chance of being dialed, so all samples of 1200 phone numbers had an equal chance of being selected. D. Systematic sampling was used, since phone numbers were selected from a list using a fixed interval between phone numbers. What potential sources of bias were present, if any? Select all that apply. A. Telephone sampling only includes people who had telephones. People who owned telephones may have been older or wealthier on average, and may not have been representative of the entire population. B. Individuals may have not been available when the researchers were calling. Those individuals that were available may have not been representative of the population. C. The sample only consisted of members of the population that were easy to get. These members may have not been representative of the population. D. Individuals may have refused to participate in the sample. This may have made the sample less representative of the population. E. There were no potential sources of bias. 22. Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Assume the population of interest is the student body at a university. Questioning students as they leave a university dorm, a researcher asks 333 students about their eating habits. What type of sampling is used? A. Systematic sampling is used, because students are selected from a list, with a fixed interval between students on the list. B. Simple random sampling is used, because students are chosen at random. C. Stratified sampling is used, because students are divided into groups, and students are chosen at random from these groups. D. Cluster sampling is used, because students are divided into groups, groups are chosen at random, and every student in one of those groups is sampled. E. Convenience sampling is used, because students are chosen due to convenience of location. What potential sources of bias are present, if any? Select all that apply. A. The sample only consists of members of the population that are easy to get. These members may not be representative of the population. B. University students may not be representative of all people in their age group. C. Because of the personal nature of the question, students may not answer honestly. D. There are no potential sources of bias. 23. Determine if the survey question is biased. If the question is biased, suggest a better wording. Why is eating cake bad for you? Is the question biased? Yes No Choose the best question below. A. Do you think that eating cake is good for you? B. How do you think eating cake affects your health? C. Why is eating cake good for you? D. Do you think that eating cake is bad for you? E. The original question is not biased. 24. Determine if the survey question is biased. If the question is biased, suggest a better wording. How often do you eat cake during an average week? Is the question biased? A. Yes, because it influences the respondent into thinking that eating cake is bad for you. B. No, because it does not lead the respondent to any particular answer. C. Yes, because it does not lead the respondent to any particular answer. D. No, because it influences the respondent into thinking that eating cake is bad for you. Choose the best question below. A. Why is eating cake bad for you? B. Do you think that eating cake is good for you? C. Do you think that eating cake is bad for you? D. The original question is not biased. 25. A company has been rating television programs for more than 60 years. It uses several sampling procedures, but its main one is to track the viewing patterns of 20,000 households. These contain more than 45,000 people and are chosen to form a cross section of the overall population. The households represent various locations, ethnic groups, and income brackets. The data gathered from the sample of 20,000 households are used to draw inferences about the population of all households in the United States. Complete parts (a) and (b) below. What strata are used in the sample? Choose the correct answer below. A. The various sampling procedures and viewing patterns B. The various locations, ethnic groups, and income brackets that are represented C. The number of households and people that are chosen D. The television ratings Why is it important to have a stratified sample for these ratings? Choose the correct answer below. A. Stratified sampling ensures that only households in the U.S. are sampled. B. Stratified sampling ensures that all of the members of one or more groups are used. C. Stratified sampling ensures that the television ratings are accurate. D. Stratified sampling ensures that each segment of the population is represented. 26. Observational studies are sometimes referred to as natural experiments. Explain what this means. Choose the correct answer below. A. In an observational study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions. B. In an observational study, a treatment is applied to part of a population and responses are obvserved. C. In an observational study, subjects are paired up according to a similarity. D. In an observational study, subjects are assigned to different treatments groups through random selection. 27. Some polling agencies ask people to call a telephone number and give their response to a question. (a) List an advantage and a disadvantage of a survey conducted in this manner. (b) What sampling technique is used in such a survey? (a) What is an advantage of this type of survey? Choose the correct answer below. A. No biases are created since anyone within the population can participate. B. This usually results in a savings in the survey cost. C. This type of survey allows for people to reply more than once. D. Using this type of method ensures that each segment of the population is represented. What is a disadvantage of this type of survey? Choose the correct answer below. A. This method of sampling can only be completed over the telephone. B. This type of survey is often very difficult to complete. C. Using this method forces the researcher to contact the sampling population directly. D. There tends to be a lower response rate and this may introduce a bias into the sample. Only a certain segment of the population might respond. (b) Identify the sampling technique used. Choose the correct answer below. A. Stratified sampling B. Convenience sampling C. Cluster sampling D. Systematic sampling 28. What is the difference between a frequency polygon and an ogive? Choose the correct answer below. A. A frequency polygon is a line graph while an ogive is a histogram. B. A frequency polygon displays class frequencies while an ogive displays cumulative frequencies. C. It is easier to find patterns in the data from a frequency polygon than an ogive. D. There is no difference between a frequency polygon and an ogive. 29. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In a frequency distribution, the class width is the distance between the lower and upper limits of a class. Choose the correct answer below. A. False. In a frequency distribution, the class width is the distance between the lower or upper limits of consecutive classes. B. False. In a frequency distribution, the range is the distance between the lower and upper limits of a class. C. True. 30. Use the given frequency distribution to find the Temperature (°F) Frequency (a) class width. 35-39 1 (b) class midpoints. 40-44 3 (c) class boundaries. 45-49 5 50-54 11 55-59 7 60-64 7 65-69 1 (a) What is the class width? 5 (Type an integer or a decimal.) (b) What are the class midpoints? Complete the table below. (Type integers or decimals.) Temperature (°F) Frequency Midpoint 35-39 1 37 40-44 3 42 45-49 5 47 50-54 11 52 55-59 7 57 60-64 7 62 65-69 1 67 (c) What are the class boundaries? Complete the table below. (Type integers or decimals.) Temperature (°F) Frequency Class boundaries 35-39 1 40-44 3 45-49 5 50-54 11 55-59 7 60-64 7 65-69 1 69.5 33. The data set below contains information about the number of children of world leaders. Use the data to construct a frequency distribution using six classes and to create a frequency polygon. 1 Click the icon to view the data set. a. Fill in the table below. Class Frequency - - - - - - b. Choose the correct graph below. A. B. C. D. 14 12 10 8 6 4 2 0 -2 4 10 16 14 12 10 8 6 4 2 0 -2 4 10 16 14 12 10 8 6 4 2 0 -2 4 10 16 14 12 10 8 6 4 2 0 -2 4 10 16 1: Data Table Number of Children 13 4 1 14 9 16 4 13 2 15 16 9 15 13 4 8 0 15 0 3 7 4 6 0 13 13 14 0 1 12 7 8 6 2 16 15 8 11 13 7 8 6 14 34. Use a stem-and-leaf plot to display the data. The data represent the heights of eruptions by a geyser. What can you conclude about the data? 127 90 110 150 140 120 100 130 110 126 136 117 115 123 129 120 133 130 109 147 Choose the correct stem-and-leaf plot. (Key: 15 | 5 = 155) A. B. C. What can you conclude about the data? A. It appears that most eruptions have a height of around 120. B. It appears that most eruptions have a height less than 140. C. It appears that most eruptions have a height of around 12. D. It appears that most eruptions have a height greater than 120. E. It appears that most eruptions have a height between 11 and 13. 35. An auction company sold 15 handheld computers last month. The final prices (in dollars) at which the items sold are as follows. 221, 242, 229, 214, 234, 246, 242, 242, 210, 255, 221, 206, 239, 229, 246 a. Construct a stem-and-leaf plot. b. Summarize what this plot tells you about the data. a. Determine the leaves in the stem-and-leaf plot shown at the right. (Use ascending order.) b. Which of the following best summarizes what the stem-and-leaf plot tells you about the data? A. The plot gives an overview of all the data. It clearly shows that the prices fall between $200 and $260 inclusive. B. The plot does not show all the data. It only shows the prices that fall between $206 and $255 inclusive. C. The plot gives an overview of all the data. It clearly shows that the prices fall between $206 and $255 inclusive. D. The plot does not show all the data. It only shows the prices that fall between $200 and $260 inclusive. 36. A study was conducted to determine how people get jobs. The table lists data from 400 randomly selected subjects. Construct a Pareto chart that corresponds to the given data. If someone would like to get a job, what seems to be the most effective approach? Choose the correct Pareto chart. A. B. C. D. 350 300 250 200 150 100 50 0 H E N M 350 300 250 200 150 100 50 0 N H E M 350 300 250 200 150 100 50 0 N H E M 350 300 250 200 150 100 50 0 H E N M If someone would like to get a job, what seems to be the most effective approach? A. Executive search firms (E) B. Mass mailing (M) C. Networking (N) D. Help-wanted ads (H) 37. A misleading graph is a statistical graph that is not drawn appropriately. This type of graph can misrepresent data and lead to false conclusions. (a) Explain why the graph is misleading. (b) Redraw the graph so that it is not misleading. (a) Choose the correct answer below. A. The large gap in the vertical axis makes it appear that the sales for the 3rd quarter are disproportionately larger than the other quarters. B. There is a gap between the quarter values. C. The quarters displayed out of order. D. The area for the 3rd quarter sales is drawn artificially larger than the area for the other quarters. (b) Choose the correct graph below. A. B. C. The durations (in minutes) of power failures at a residence in the last 4 years are listed below. 13 65 13 59 52 39 23 82 39 112 What is the mean duration? Select the correct choice below and fill in any answer box to complete your choice. A. The mean duration is 49.7 minutes. (Round to one decimal place as needed.) B. There is no mean score. Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is not a data value. C. The mean does not represent the center because it is the largest data value. D. The mean does not represent the center because it is the smallest data value. What is the median duration? Select the correct choice below and fill in any answer box to complete your choice. A. The median duration is 45.5 minutes. (Round to one decimal place as needed.) B. There is no median score. Does the median represent the center of the data? A. The median represents the center. B. The median does not represent the center because it is the smallest data value. C. The median does not represent the center because it is the largest data value. D. The median does not represent the center because it is not a data value. What is the mode of the durations? Select the correct choice below and fill in any answer box to complete your choice. A. The mode(s) of the durations is (are) 13,39 minutes. (Use a comma to separate answers as needed.) B. There is no mode. Does (Do) the mode(s) represent the center of the data? A. The mode(s) represent(s) the center. B. The mode(s) does (do) not represent the center because it (one) is the largest data value. C. The mode(s) can't represent the center because it (they) is (are) not a data value. D. The mode(s) does (do) not represent the center because it (one) is the smallest data value. The typing speeds (in words per minute) for several stenographers are listed below. 240 185 240 225 150 190 125 205 155 139 What is the mean typing speed? Select the correct choice below and fill in any answer box to complete your choice. A. The mean typing speed is 185.4 words per minute. (Round to one decimal place as needed.) B. There is no mean score. Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is not a data value. C. The mean does not represent the center because it is the smallest data value. D. The mean does not represent the center because it is the largest data value. What is the median typing speed? Select the correct choice below and fill in any answer box to complete your choice. A. The median typing speed is 187.5 words per minute. (Round to one decimal place as needed.) B. There is no median score. Does the median represent the center of the data? A. The median represents the center. B. The median does not represent the center because it is the smallest data value. C. The median does not represent the center because it is the largest data value. D. The median does not represent the center because it is not a data value. What is the mode of the typing speeds? Select the correct choice below and fill in any answer box to complete your choice. A. The mode(s) of the typing speeds is (are) 240 words per minute. (Use a comma to separate answers as needed.) B. There is no mode. Does (Do) the mode(s) represent the center of the data? A. The mode(s) represent(s) the center. B. The mode(s) does (do) not represent the center because it (one) is the smallest data value. C. The mode(s) can't represent the center because it (they) is (are) not a data value. D. The mode(s) does (do) not represent the center because it (one) is the largest data value. YOU ANSWERED: A.: 170.0 40. Without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning. Do You Send "Thank You" Notes After a Job Interview? 200 150 100 50 0 Choose the correct answer below. A B C D A. The mean is the best measure because the data are skewed. B. The mode is the best measure because the data are at the nominal level of measurement. C. The mean is the best measure because the data are approximately symmetric. D. The median is the best measure because the data are skewed or have an outlier. 41. The scores and their percents of Score Percent of Weighted The student's new weighted mean score is (Simplify your answer.) 85.45 . 42. The numbers of days 20 patients remained hospitalized are shown below. Construct a frequency distribution of the data using 6 classes. 6 9 7 14 4 5 6 8 4 11 10 6 8 6 5 7 6 6 3 11 Construct a frequency distribution and a frequency histogram of the data using 6 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. Choose the correct histogram below. A. Frequency 10 8 6 4 2 0 3.5 9.5 Days B. Frequency 10 8 6 4 2 0 3.5 9.5 Days Hospitalization Hospitalization C. Frequency 10 8 6 4 2 0 3.5 9.5 Days D. Frequency 10 8 6 4 2 0 3.5 9.5 Days Hospitalization Hospitalization Describe the shape of the histogram. Choose the correct answer below. A. Uniform B. Symmetric C. Positively skewed D. Negatively skewed E. None of these YOU ANSWERED: 9 3 43. During a quality assurance check, the actual coffee content (a) The mean coffee content is 6.012 ounces. (in ounces) of six jars of instant coffee was recorded as 6.03, 5.63, 6.40, 6.00, 5.99, and 6.02. (Round to three decimal places as needed.) (a) Find the mean and the median of the coffee content. The median coffee content is 6.010 ounces. (b) The third value was incorrectly measured and is actually 6.04. Find the (Round to three decimal places as needed.) (b) After correcting the data error, the mean coffee content mean and median of the coffee content again. is 5.952 ounces. (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error? (Round to three decimal places as needed.) After correcting the data error, the median coffee content is ounces. (Round to three decimal places as needed.) (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error? Median Mean YOU ANSWERED: 6.04 6.02 6.020 44. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are given. Complete parts (a) through (c) below. 24 23 54 37 36 27 29 47 47 15 19 31 34 35 23 26 12 17 11 42 37 53 24 16 27 18 18 42 24 34 (a) Find the mean and median of the data. The mean is . (Round to three decimal places as needed.) The median is . (Type an integer or a decimal.) (b) Draw a stem-and-leaf plot for the data using one row per stem. Which stem-and-leaf plot below shows the data? A. 1 2 3 4 5 B. 1 34 2 2277 3 4 5 C. 1 2 3 4 2277 5 34 D. 1 1467 2 3 4 5 3357 (c) Describe the shape of the distribution. Which description below best describes the shape of the distribution? A. The distribution is skewed right (positively skewed). B. The distribution is skewed left (negatively skewed). C. The distribution is uniform. D. The distribution is symmetric. 45. Both data sets have a mean of 245. One has a standard deviation of 16, and the other has a standard deviation of 24. 2 Click the icon to view data sets. Which data set has which deviation? A. (a) has a standard deviation of 24 and (b) has a standard deviation of 16, because the data in (a) have more variability. B. (a) has a standard deviation of 16 and (b) has a standard deviation of 24, because the data in (b) have less variability. 2: Data Table 46. Compare the three data sets on the right. (i) 7 (ii) 7 (iii) 7 0 3 45 67 Data value 0 d25 3 45 67 Data value d36 0 3 45 67 Data value (a) Which data set has the greatest sample standard deviation? A. Data set (ii), because it has more entries that are farther away from the mean. B. Data set (iii), because it contains the greater number of entries. C. Data set (i), because its data have more variability. Which data set has the least sample standard deviation? A. Data set (iii), because it has more entries that are close to the mean. B. Data set (ii), because it has no entries near the mean. C. Data set (i) because it has more entries near the mean than far away from it. (b) How are the data sets the same? How do they differ? A. The three data sets have the same standard deviations but have different ranges. B. The three data sets have the same range but have different means. C. The three data sets have the same range and mean but have different standard deviations. D. The three data sets have the same mean but have different standard deviations. 47. You used SS = Σ x − x 2 when calculating variance and standard deviation. An alternative formula for the standard deviation that is sometimes convenient for hand calculations is shown below. You can find the sample variance by dividing the sum of squares by n − 1, and the sample standard deviation by finding the square root of the sample variance. Complete parts (a) and (b) below. (Σx)2 SS = Σx2 − n 3 Click the icon for a table of the ages (in years) of shoppers at a local store. (a) Use the shortcut formula to calculate the sample standard deviation. s = (Simplify your answer. Round to one decimal place as needed.) (b) Find the sample standard deviation using the usual formula of s = (a). , and compare it to your result from part The sample standard deviation is . This is (1) the result from part (a). (Simplify your answer. Round to one decimal place as needed.) 3: Shoppers' Ages (1) greater than equal to less than Shoppers' Ages 14 17 15 24 19 16 18 14 15 20 18 16 21 14 16 19 18 22 16 14 48. Sample annual salaries (in thousands of dollars) for employees at a company are listed. 30 35 51 49 33 62 35 45 (a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a 5% raise. Find the sample mean and sample standard deviation for the revised data set. (c) To calculate the monthly salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)? (a) The sample mean is x = (Round to one decimal place as needed.) The sample standard deviation is s = (Round to one decimal place as needed.) (b) The sample mean is x = (Round to one decimal place as needed.) The sample standard deviation is s = (Round to one decimal place as needed.) (c) The sample mean is x = (Round to one decimal place as needed.) The sample standard deviation is s = (Round to one decimal place as needed.) thousand dollars. thousand dollars. thousand dollars. thousand dollars. thousand dollars. thousand dollars. (d) What can you conclude from the results of (a), (b), and (c)? A. When each entry is multiplied by a constant k, the new sample mean is k • x and the sample standard deviation remains unaffected. B. When each entry is multiplied by a constant k, the new sample mean is k • x and the new sample standard deviation is k • s. C. When each entry is multiplied by a constant k, the sample mean and the sample standard deviation remain unaffected. D. When each entry is multiplied by a constant k, the new sample standard deviation is k • s and the sample mean remains unaffected. 49. Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are greater than Q3 + 1.5(IQR) or less than Q1 − 1.5(IQR) are considered outliers. 50. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The 50th percentile is equivalent to Q1 . Choose the correct answer below. A. The statement is false. The 50th percentile is equivalent to Q3 . B. The statement is false. The 50th percentile is equivalent to the mean. C. The statement is true. D. The statement is false. The 50th percentile is equivalent to Q2 . 51. Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. a. Find the quartiles. The first quartile, Q1 , is . The second quartile, Q2 , is . The third quartile, Q3 , is . (Type integers or decimals.) b. Find the interquartile range. The interquartile range (IQR) is . (Type an integer or a decimal.) c. Identify any outliers. Choose the correct answer below. A. There exists at least one outlier in the data set at . (Use a comma to separate answers as needed.) B. There are no outliers in the data set. 52. (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 4 8 8 6 2 9 8 7 9 6 9 5 2 6 2 9 8 7 7 9 (a) Min = 2 (Simplify your answer.) Q1 = 6 (Simplify your answer. Do not round.) Q2 = 7 (Simplify your answer. Do not round.) Q3 = 9 (Simplify your answer. Do not round.) Max = 9 (Simplify your answer.) (b) Choose the correct box-and-whisker plot below. A. B. C. D. 53. (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 3 8 8 6 2 9 8 7 9 6 9 5 2 6 2 9 8 7 7 9 (a) Min = 2 (Simplify your answer.) Q1 = 6 (Simplify your answer. Do not round.) Q2 = 7 (Simplify your answer. Do not round.) Q3 = 9 (Simplify your answer. Do not round.) Max = 9 (Simplify your answer.) (b) Choose the correct box-and-whisker plot below. A. B. C. D. 54. A modified boxplot is a boxplot that uses symbols to identify outliers. The horizontal line of a modified boxplot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. (a) Identify any outliers and (b) draw a modified boxplot that represents the data set. Use a cross ( × ) to plot any outliers. 40 46 39 (a) Identify any possible outliers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The outlier(s) is(are) 22,82 . (Type an integer or decimal. Use a comma to separate answers as needed.) B. There are no outliers. (b) Choose the correct boxplot of the data below. A. B. C. D. 100 100 100 100