Math 146 Statistics for the Health Sciences Additional Exercises on Chapter 2 Student Name: Solve the problem. 1) Scott Tarnowski owns a pet grooming shop. His prices for grooming dogs are based on the size of the dog. His records from last year are summarized below. Class Frequency Large 345 Medium 830 Small 645 Construct a frequency table including relative frequencies and percentages. 2) The preschool children at Elmwood Elementary School were asked to name their favorite color. The results are listed below. purple purple green yellow blue blue blue purple blue green blue green yellow yellow yellow green blue yellow blue red Construct a frequency distribution and a relative frequency distribution. The bar graph shows the number of tickets sold each week by the garden club for their annual flower show. 3) During which week was the most number of tickets sold? 4) How many tickets were sold during week 1? 1
Solve the problem. 5) Retailers are always interested in determining why a customer selected their store to make a purchase. A sporting goods retailer conducted a customer survey to determine why its customers shopped at the store. The results are shown here. What percentage of the customers responded that the merchandise was the reason they shopped at the store? The Excel frequency bar graph below describes the employment status of a random sample of U.S. adults. Use the bar graph to answer the question. 6) What is the percentage of those having no job? Solve the problem. 7) Scott Tarnowski owns a pet grooming shop. His prices for grooming dogs are based on the size of the dog. His records from last year are summarized below. Class Frequency Large 345 Medium 830 Small 645 Portray the data in a pie chart using the class percentages. 2
8) The grade point averages for 40 students are listed below. Construct a grouped-data table using eight classes. Use 0.5 as the lower limit of the first class. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 3.1 2.4 2.4 2.3 1.6 1.6 4.0 3.1 3.2 1.8 2.2 2.2 1.7 0.5 3.6 3.4 1.9 2.0 3.0 1.1 3.0 4.0 4.0 2.1 1.9 1.1 0.5 3.2 3.0 2.2 9) The Highway Patrol, using radar, checked the speeds (in mph) of 30 passing motorists at a checkpoint. The results are listed below. Construct a grouped-data table using six classes. Use 30 as the lower limit of the first class. 44 38 41 50 36 36 43 42 49 48 35 40 37 41 43 50 45 45 39 38 50 41 47 36 35 40 42 43 48 33 10) The class width is the difference between 11) The heights (in inches) of 30 adult males are listed below. Construct a grouped-data table using five classes. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 69 71 68 67 73 74 70 71 69 68 12) A sample of 15 measurements follow: 97 120 137 124 117 108 134 126 123 106 130 110 100 120 140 Construct a frequency histogram for the data using a class interval width of 10 and the lower boundary of the first class is 95. 13) The heights (in inches) of 30 adult males are listed below. Construct a stem-and-leaf chart for the data. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 69 71 68 67 73 74 70 71 69 68 14) The Highway Patrol, using radar, checked the speeds (in mph) of 30 passing motorists at a checkpoint. The results are listed below. Construct a stem-and-leaf plot for the data. 44 38 41 50 36 36 43 42 49 48 35 40 37 41 43 50 45 45 39 38 50 41 47 36 35 40 42 43 48 33 3
15) The Highway Patrol, using radar, checked the speeds (in mph) of 30 passing motorists at a checkpoint. The results are listed below. Construct a dot plot for the data. 44 38 41 50 36 36 43 42 49 48 35 40 37 41 43 50 45 54 39 38 50 41 47 36 35 40 42 43 48 33 16) The following data represent the bachelor degrees of CEO's at area small businesses. Determine the mode degree. Degree Number Accounting 29 Business 46 Liberal Arts 10 Marketing 22 Other 8 17) Find the mean, median, and mode of the following numbers: 88 91 84 88 81 89 88 82 83 86 18) The scores of the top ten finishers in a recent LPGA Valley of the Stars Tournament are listed below. (Source: Los Angeles Times) Find the mean score. 71 67 67 72 76 72 73 68 72 72 19) The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the median speed. 181.1 202.2 190.1 201.4 191.3 201.4 192.2 201.2 193.2 201.2 194.5 199.2 196.0 196.2 20) A student receives test scores of 62, 83, and 91. The student's final exam score is 88 and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% of the final grade. What is the student's mean score in the class? 21) Find the mean, median, and mode of the following numbers: 90 93 86 90 83 91 90 84 85 88 4
22) The numbers of home runs that a baseball player hit in the first 13 years of his major league baseball career are listed below. 3 49 32 33 39 22 42 9 9 39 52 58 70 Find the mean and median number of home runs. Round the mean to the nearest whole number. 23) The scores of the top ten finishers in a women's golf tournament are listed below. 71 67 67 72 76 72 73 68 72 72 Find the median score. 24) The scores of the top ten finishers in a women's golf tournament are listed below. 71 67 67 72 76 72 73 68 72 72 Find the mode score. 25) Calculate the mean, median, and mode for the following sample: 5, 10, 6, 11, 0, 0, 10, 0. Find the range for the group of data items. 26) 9, 10, 11, 12, 13 27) 6, 19, 6, 19, 6, 19, 6, 19 Find the sample standard deviation for the group of data items (to the nearest hundredth). 28) 6, 6, 6, 9, 12, 12, 12 Solve the problem. 29) The heights (in inches) of 20 adult males are listed below. Find the range of the data. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 30) The heights (in inches) of 10 adult males are listed below. Find the population standard deviation and the population variance. 70 72 71 70 69 73 69 68 70 71 31) In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed below. Compute the range, sample standard deviation and sample variance of the data. 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8 5
Find the sample standard deviation. Round to one more place than the data. 32) 18, 20, 13, 15, 9, 18, 13, 8, 17 33) 173, 209, 283, 183, 251, 167, 112, 258, 211 34) 4, 1, 14, 7, 12, 18, 8, 10, 11 Solve the problem. 35) For the stem-and-leaf plot below, find the range of the data set. 1 4 5 2 6 6 6 7 8 9 2 7 7 7 8 8 9 9 9 3 0 1 1 2 3 4 4 5 3 6 6 6 7 8 8 9 4 0 0 36) The grade point averages for 10 students are listed below. Find the range of the data. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 37) The heights (in inches) of 10 adult males are listed below. Find the sample standard deviation. 70 72 71 70 69 73 69 68 70 71 38) In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed below. Compute the range, sample standard deviation and sample variance of the data. 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8 39) In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed below. Compute the coefficient of variation. 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8 40) Eleven high school teachers were asked to give the numbers of students in their classes. The sample data follows: 36, 31, 30, 31, 20, 19, 24, 34, 21, 28, 24. Find the five-number summary. 6
41) The test scores of 30 students are listed below. Draw a boxplot that represents the data. 31 41 45 48 52 55 56 56 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99 42) The test scores of 30 students are listed below. Find the five number summary and draw a boxplot. 31 41 45 48 52 55 56 56 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99 43) The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find the five number summary and draw a boxplot. 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265 7
Answer Key Testname: MATH 146 ADDITIONAL EXERCISES ON CHAPTER 2 1) Class Frequency Relative Frequency Percentage Large 345.190 19.0 Medium 830.456 45.6 Small 645.354 35.4 Total 1820 1.000 100.0 2) Color Frequency Relative Frequency purple 3 0.15 green 4 0.20 yellow 5 0.25 blue 7 0.35 red 1 0.05 3) Week 4 4) 46 tickets 5) 42.9% 6) 15% 7) 8) GPA Frequency Relative Frequency 0.5-0.9 1.0-1.4 1.5-1.9 2.0-2.4 2.5-2.9 3.0-3.4 3.5-3.9 4.0-4.4 4 2 7 9 2 10 2 4 0.10 0.05 0.175 0.225 0.05 0.25 0.05 0.10 9) Speed (in mph) Frequency Relative Frequency 33-35 36-38 39-41 42-44 45-47 48-50 3 6 6 6 3 6 0.10 0.20 0.20 0.20 0.10 0.20 10) Two successive lower class limits 8
Answer Key Testname: MATH 146 ADDITIONAL EXERCISES ON CHAPTER 2 11) 12) 13) 14) 6 7 7 8 8 8 8 9 9 9 9 9 7 0 0 0 0 0 1 1 1 1 1 1 1 1 2 2 3 3 4 4 3 3 5 5 6 6 6 7 8 8 9 4 0 0 1 1 1 2 2 3 3 3 4 5 5 7 8 8 9 5 0 0 0 9
Answer Key Testname: MATH 146 ADDITIONAL EXERCISES ON CHAPTER 2 15) 16) business 17) mean 86, median 87, mode 88 18) 71 19) 196.1 20) 80.6 21) mean 88, median 89, mode 90 22) mean: 35; median 39 23) 72 24) 72 25) mean = 5.25, median = 5.5, mode = 0 26) 4 27) 13 28) 3 29) 7 30) σ = 1.42, σ2 = 2.01 31) range = 4.4, s = 1.8, s2 = 3.324 32) 4.2 33) 53.2 34) 5.2 35) 26 36) 3.2 37) 1.49 38) range = 4.4, s = 1.8, s2 = 3.324 39) coefficient of variation = 1.82 100% = 58.3% 3.12 40) 19, 21, 28, 31, 36 10
Answer Key Testname: MATH 146 ADDITIONAL EXERCISES ON CHAPTER 2 41) 42) 83 43) 180 11