Elementary Math Exam

1. Maria is completing a survey to use for a project in her statistics class. She went to two local stores and asked 10 randomly selected patrons to give their ages. The data she collected is shown below. Store 1:   42, 30, 26, 28, 39, 30, 15, 60, 39, 85 Store 2: 79, 59, 67, 89, 68, 79, 79, 67, 85, 91 How does the mode of Maria's data at Store 1 differ from the mode at Store 2? A. The mode of Maria's data at Store 1 is   less than the mode at Store 2 by 28. B. The mode of Maria's data at Store 1 is greater than the mode at Store 2 by 28. C. The mode of Maria's data at Store 1 is less than the mode at Store 2 by 49. D. The mode of Maria's data at Store 1 is greater than the mode at Store 2 by 49. 2. Michael and Stanley both work for the same company in sales. Their supervisor announced that the salesperson with the highest   cumulative sales numbers over the last six months will receive a bonus. Below is a table showing the worth of the goods sold by Michael and Stanley for each of the last six months.   | Month | Michael | Stanley | |---|---|---| | March | $57,809.00 | $47,156.00 | | April | $64,421.00 | $56,373.00 | | May | $69,398.00 | $53,596.00 | | June | $61,524.00 | $54,804.00 | | July | $55,688.00 | $58,586.00 | | August | $46,339.00 | $55,358.00 | How does the range of Michael's sales numbers compare to the range of Stanley's sales numbers? A. The range of Michael's sales numbers is greater than the range of Stanley's sales numbers by $5,677.00. B. The range of Michael's sales numbers is   greater than the range of Stanley's sales numbers by $8,691.00. C. The range of Michael's sales numbers is less than the range of Stanley's sales numbers by $8,691.00. D. The range of Michael's sales numbers is less than the range   of Stanley's sales numbers by $8,883.00. Michael: 69,398 - 46,339 = 23,059   Stanley: 61,524 - 47,156 = 14,368 8,691 3. A company conducted a survey of 6,225 people to find out the fastest speed they have driven in certain cities. Based on the table below, what is the difference   between the sample's interquartile range and the population's interquartile range? | Name | Minimum | 1st Quartile | 2nd Quartile | 3rd Quartile | Maximum   | |---|---|---|---|---|---| | Atlanta | 70 | 84 | 90 | 103 | 112 | | Athens | 69 | 78 | 95 | 107 | 114 | | Chickamauga | 75 | 80 | 86 | 97 | 105 | | Gray | 75 | 87 | 86 | 109 | 119 | | Population | 68 | 74 | 94 | 111   | 127 | **Find the average Interquartile Range for the sample:** Atlanta: 103 - 84 = 19 Athens: 107 - 78 = 29 Chickamauga: 97 - 80 = 17 Gray: 109 - 87 = 22 (19 + 29 + 17 + 22) / 4 = 21.75 Interquartile Range of Population: 111 - 74 = 37 37 - 21.75 = 15.25 **Answer: C. There is a difference of 15.25.** 4. Mr. and Mrs. Nelson have decided they are going to send their son, Christopher, to a private high school. They will make their decision based on a rating system where 1 point is the lowest score a school can receive and 20 points is the highest. Below are the ratings received by the schools over a five-year period.   | School | 2002 | 2003 | 2004 | 2005 | 2006 | |---|---|---|---|---|---| | Sunlight Academy | 12 | 11 | 14 | 13 | 10 | | Shadow Ridge Preparatory | 17 | 14 | 11 | 12 | 16 | Based on the mean of the ratings, which school should the Nelsons choose and why? A. Sunlight Academy, because its mean rating   is 2 points higher. B. Shadow Ridge Preparatory, because its mean rating is 3 points higher. C. Shadow Ridge Preparatory, because its mean rating is 2 points higher. D. Sunlight Academy, because its mean rating is 3 points higher.   Sunlight Academy: (12+11+14+13+10)/5 = 12 Shadow Ridge Preparatory: (17+14+11+12+16)/5 = 14 14 - 12 = 2 **Answer: C. Shadow Ridge Preparatory, because its mean rating is 2 points higher.** C. Raul bought 4 new movies with lengths of 126, 116, 104, and 134 minutes. Find the new interquartile range and the new mean length of the shortest 25% of the movies. 1   9 2 3 6 6 7 8 8 8 9 10 1 2 3 4 5 5 6 7 8 9 11 1 2 2 3 4 5 6 7 8 9 12 1 2 2 3 4 5 6 7 9 13 0 1 4 6 14 3 7 15 8 Q3 - Q1 = 126 - 103 = 23 Interquartile range: 23 minutes mean of the shortest 25%: 97.6 minutes (92+93+96+96+97+98+98+101+102+103) / 10 = 976 / 10 = 97.6 5. The school is conducting a survey to determine the relationship between the outside temperature and the number of students who eat lunch in the outside commons. The information is in the chart below. 1   | Temperature (°F) | Number of Students | |---|---| | 57 | 44 | | 65 | 92 | | 66 | 361 | | 57 | 176 | | 73 | 124 | | 71 | 361 | | 91 | 294 | What is the approximate mean of the temperatures? average = (57 + 65 + 66 + 57 + 73 + 71 + 91) / 7 = 68.57 A. 69.00°F B. 70.50°F C. 80.00°F D. 68.57°F 6. 46, 51, 54, 56, 58, 60, 64, 69, 70, 74, 74 Which of the box-and-whisker plots below represents the data set above? The four dots represent the minimum, 1st quartile, median, 2nd quartile, and maximum values.