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Math 227 – Elementary Statistics: A Brief Version, 5/e Bluman Section 2-1 #’s 3, 7, 8, 11 3) Find the class boundaries, midpoints, and widths for each class. a) 12 – 18 7) b) 56 – 74 c) 695 – 705 Class Limits 12 – 18 Class Boundaries 11.5 – 18.5 56 – 74 55.5 – 74.5 695 – 705 694.5 – 705.5 13.6 – 14.7 13.55 – 14.75 2.15 – 3.93 2.145 – 3.935 d) 13.6 – 14.7 e) 2.15 – 3.93 Midpoints 12 + 18 = 2 56 + 74 = 2 695 + 705 = 2 13.6 + 14.7 = 2 2.15 + 3.93 = 2 30 = 15 2 130 = 65 2 1400 = 700 2 28.3 = 14.15 2 6.08 = 3.04 2 Class Width 7 19 11 1.2 1.79 Trust in Internet Information A survey was taken on how much trust people place in the information they read on the Internet. Construct a categorical frequency distribution for the data. A = trust in everything they read, M = trust in most of what they read, H = trust in about one-half of what they read, S = trust in a small portion of what they read. M M M A H M S M H M S M M M M A M M A M M M H M M M H M H M A M M M H M M M M M Class Limit A Frequency f 4 M 28 H 6 S 2 Total 40 Percent % 4 = 0.10 = 10% 40 28 = 0.70 = 70% 40 6 = 0.15 = 15% 40 2 = 0.05 = 5% 40 100 % 8) State Gasoline Tax The state gas tax in cents per gallon for 25 states is given below. Construct a grouped frequency distribution and a cumulative frequency distribution with 5 classes. 7.5 21.5 22 23 14.5 16 19 20.7 18.5 25.9 23.5 20 17 25.3 18 17 27.1 28 24 30 22 20 20 31 31.5 Range = 31.5-7.5 = 24 ; # of classes = 5; class width= Class Limits Boundaries Frequency f Cf 7.5 - 12.4 12.5 - 17.4 17.5 - 22.4 22.5 - 27.4 27.5 - 32.4 7.45 - 12.45 12.45 - 17.45 17.45 - 22.45 22.45 - 27.45 27.45 - 32.45 1 4 10 6 4 25 1 5 15 21 25 Total 11) 24 = 4.8 or 5 5 GRE Scores at Top-Ranked Engineering Schools The average quantitative GRE scores for the top 30 graduate schools of engineering are listed. Construct a frequency distribution with 6 classes. 767 770 761 760 771 768 776 771 756 770 763 760 747 766 754 771 771 778 766 762 780 750 746 764 769 759 757 753 758 746 H = 780 ; L = 746 ; Range = 780 – 746 = 34 ; # of classes = 6 ; class width = Round up ( 34 )= 6 Round up ( 5.6 ) = 6 Class Limits 746 – 751 752 – 757 758 – 763 764 – 769 770 – 775 776 – 781 Frequency f 4 4 7 6 6 3 Boundaries 745.5 – 751.5 751.5 – 757.5 757.5 – 763.5 763.5 – 769.5 769.5 – 775.5 775.5 – 781.5 Cf 4 8 15 21 27 30 Mid-point 748.5 754.5 760.5 766.5 772.5 778.8 Section 2-2 #’s 4, 5, 15, 16 4) NFL Salaries The salaries (in millions of dollars) for 31 NFL teams for a specific season are given in this frequency distribution. Class limits Frequency Cf Mid-point 39.9–42.8 2 2 41.35 42.9–45.8 2 4 44.35 45.9–48.8 5 9 47.35 48.9–51.8 5 14 50.35 51.9–54.8 12 26 53.35 54.9–57.8 5 31 56.35 Construct a histogram, a frequency polygon, and an ogive for the data; and comment on the shape of the distribution. a) Histogram: b) Frequency Polygon: c) Ogive: The distribution is left skewed or negatively skewed. 5) Automobile Fuel Efficiency Thirty automobiles were tested for fuel efficiency, in miles per gallon (mpg). The following frequency distribution was obtained. Construct a histogram, frequency polygon, and ogive for the data. Class boundaries Frequency Cf Midpoint 7.5 – 12.5 3 3 10 12.5 – 17.5 5 8 15 17.5 – 22.5 15 23 20 22.5 – 27.5 5 28 25 27.5 – 32.5 2 30 30 a) Histogram: b) Frequency Polygon: c) Ogive: 15) Cereal Calories The number of calories per serving for selected ready-to-eat cereals is listed here. Construct a frequency distribution using 7 classes. Draw a histogram, frequency polygon, and ogive for the data, using relative frequencies. Describe the shape of the histogram. 130 190 140 80 100 120 220 220 110 100 210 130 100 90 210 120 200 120 180 120 190 210 120 200 130 180 260 270 100 160 190 240 80 120 90 190 200 210 190 180 115 210 110 225 190 130 L = 80 ; H = 270 ; Range = 270 – 80 = 190 ; # of classes = 7 ; Class width = Roundup ( Roundup ( 27.14) = 28 Class Limits 80 – 107 108 – 135 136 – 163 164 – 191 192 – 219 220 – 249 248 - 275 Total a) Histogram: Frequency 8 13 2 9 8 4 2 46 Boundaries 79.5 – 107.5 107.5 -135.5 135.5 – 163.5 163.5 – 191.5 191.5 – 219.5 219.5 – 247.5 247.5 -275.5 Cf 8 21 23 32 40 44 46 Rf % 17% 28% 4% 20% 17% 8% 4% 190 )= 7 The Histogram has 2 peaks. b) Frequency Polygon: c) Ogive: 16) Protein Grams in Fast Food The amount of protein (in grams) for a variety of fast-food sandwiches is reported here. Construct a frequency distribution using 6 classes. Draw a histogram, frequency polygon, and ogive for the data, using relative frequencies. Describe the shape of the histogram. 23 30 20 27 44 26 35 20 29 29 25 15 18 27 19 22 12 26 34 15 27 35 26 43 35 14 24 12 23 31 40 35 38 57 22 42 24 21 27 33 L = 12 ; H = 57 ; Range = 57 – 12 = 45 ; # of classes = 6 ; Class width = Roundup ( Class Limits 12 – 19 Frequency 7 Boundaries 11.5 – 19.5 Mid-point 15.5 Cf 7 20 – 27 17 19.5 – 27.5 23.5 24 28 – 35 10 27.5 – 35.5 31.5 34 36 – 43 4 35.5 – 43.5 39.5 38 44 – 51 1 43.5 – 51.5 47.5 39 52 – 59 1 51.5 – 59.5 55.5 40 Total 40 a) Histogram: 45 ) = Roundup ( 7.5) = 8 6 Rf % 7 = 0.175 = 18% 40 17 = 0.425 = 43% 40 10 = 0.25 = 25% 40 4 = 0.1 = 10% 40 1 = 0.025 = 3% 40 1 = 0.025 = 3% 40 b) Frequency Polygon: c) Ogive: Section 2-3 #’s 3, 5, 6, 10, 14, 15, 16 3) Internet Connections The following data represent the estimated number (in millions) of computers connected to the Internet worldwide. Construct a Pareto chart for the data. Based on the data, suggest the best place to market appropriate Internet products. Location Homes Small companies Large companies Government agencies Schools Number of computers 240 102 148 33 47 The best place to market products would be to the home viewers. 5) World Energy Use The following percentages indicate the source of energy used worldwide. Construct a Pareto chart for the energy used. Petroleum Coal Dry natural gas Hydroelectric Nuclear Other (wind, solar, etc.) 39.8% 23.2% 22.4% 7.0% 6.4% 1.2% 6) Airline Departures draw a time series graph to represent the data for the number of airline departures (in millions) for the given years. Over the years, is the number of departures increasing, decreasing, or about the same? Year 1996 1997 1998 1999 2000 2001 2002 Number of departures 7.9 9.9 10.5 10.9 11.0 9.8 10.1 There was an increase in the number of departures until 2000, then a decrease in 2001, and then an increase. 7) Tobacco Consumption the data represent the personal consumption (in billions of dollars) for tobacco in the United States. Draw a time series graph for the data and explain the trend. Year Amount 1995 8.5 1996 8.7 1997 9.0 1998 9.3 1999 9.6 2000 9.9 2001 10.2 2002 10.4 There is a steady increase in consumption of tobacco products. 10) Reasons We Travel The following data are based on a survey from American Travel Survey on why people travel. Construct a pie graph for the data and analyze the results. Purpose Personal business (PB) Number 146 Percent 146 = 14.6% 1000 14) Visit friends or relatives (VF) 330 Work-related (WR) 225 Leisure (L) 299 Total 1000 330 = 33.0% 1000 225 = 22.5% 1000 299 = 29.9% 1000 State which graph (Pareto chart, time series graph, or pie graph) would most appropriately represent the given situation. a) The number of students enrolled at a local college for each year during the last 5 years. Answer: Time series graph b) The budget for the student activities department at a certain college for each year during the last 5 years. Answer: Pie graph c) The means of transportation the students use to get to school. Answer: Pareto chart d) The percentage of votes each of the four candidates received in the last election. Answer: Pie graph e) The record temperature of a city for the last 30 years. Answer: Time series graph f) The frequency of each type of crime committed in a city during the year. Answer: Pareto chart 15) President’s Ages at Inauguration The age at inauguration for each U.S. President is shown. Construct a stem and leaf plot and analyze the data. 57 54 52 55 51 56 61 68 56 55 54 61 57 51 46 54 51 52 57 49 54 42 60 69 58 64 49 51 62 64 57 48 50 56 43 46 61 65 47 55 55 54 Double Stem and Leaf Plot The distribution is somewhat symmetric and unimodal. The majority of the Presidents were in their 50’s when inaugurated. 16) Calories in Salad Dressings A listing of calories per one ounce of selected salad dressings (not fat-free) is given below. Construct a stem and leaf plot for the data. Section 2-4 #’s 6, 7, 13 6) Hours Spent Jogging A researcher wishes to determine whether the number of hours a person jogs per week is related to the person’s age. Draw a scatter plot and comment on the nature of the relationship. Age, x 34 22 48 56 62 Hours, y 5.5 7 3.5 3 1 Stem Leaf 4 4 5 5 6 6 23 667899 011112244444 555566677778 0111244 589 7) Recreational Expenditures A study was conducted to determine if the amount a person spends per month on recreation is related to the person’s income. Draw a scatter plot and comment on the nature of the relationship. Income, x Amount, y $800 $60 $1200 $200 $1000 $160 $900 $135 $850 $45 $907 $90 $1100 $150 There appears to be a positive linear relationship between a person’s monthly income and the amount a person spends on recreation each month. 13) Absences and Final Grades An educator wants to see if there is a relationship between the number of absences a student has and his or her final grade in a course. Draw a scatter plot and comment on the nature of the relationship. Number of absences, x 10 12 2 0 8 5 Final Grade 70 65 96 94 75 82 There appears to be a negative linear relationship between the number of absences a student has and his or her final grade in a course.