1. The line of best fit for a sample of data can be determined using technology by employing the method of (two marks). 2. The table shows the fuel consumption, in litres per 100 km, for various speeds that a car is driven, in kilometres per hour. The equation for the line of best fit is Speed, s (km/h) Fuel, /(L/100 km) 50 5.0 60 5.5 70 6.1 80 6.8 90 7.7 (three marks)3. Arianna recorded data on the amount of rainfall in a given week and the depth of water in the local creek at the end of the week, as shown. Is there a cause and effect relationship? 4 3 Depth_m 2 . N - 6 10 12 Rainfall_mm Depth_m = 0.483Rainfall_mm + 0.067; r2 = 0.99 (four marks) 4. Arianna recorded data on the amount of rainfall in a given week and the depth of water in the local creek at the end of the week, as shown. The creek will overflow if the depth exceeds 6 m. What level of rainfall will result in a flood warning? (four marks)3 Depth_m N 6 8 10 12 Rainfall_mm - Depth_m = 0.483Rainfall_mm + 0.067; r2 = 0.99 5. Data collected on the daily average number of movie tickets sold in Bravoville and the average number of visits to the food bank every month for six months is shown. Suggest the likely relationship. Give an example or reason for your answer. 150 140 130 Food Bank 120 110 100 170 180 190 200 210 220 230 240 Movie_Tickets Food_Bank = -1.224Movie_Tickets + 376; r2 = 0.99 (four marks)6. A beach store sells sunglasses as well as ice cream. The table shows sales for five summer days. Is there a correlation between sales of sunglasses and sales of ice cream? Provide evidence for your answer. Sunglasses Sold Ice Cream Sold 11 45 19 80 55 225 32 125 41 162 (four marks) 7. A beach store sells sunglasses as well as ice cream. The table shows sales for five summer days. Determine the equation of the line of best fit. Sunglasses Sold, s Ice Cream Sold, c 11 45 19 80 55 225 32 125 41 162 (four marks)8. Ten students in the Data Management class were timed for a 10-km bicycle ride. The table shows the final marks in the course and times to ride 10 km, in minutes are shown. Determine the equation of the line of best fit. Math Mark, m Time, f (min) 73 64 71 58 69 56 71 53 73 55 71 66 70 62 75 59 88 65 72 71 (five marks)9. As a data management project, Raj accesses city records and compares the number of fire hydrants to the population every five years, as shown. If the population is projected to increase to 30 000, how many fire hydrants will be needed? 35- 30- 25 Population_1000s 0 20 40 60 80 100 120 140 160 180 Fire_Hydrants Population_1000s = 0.0998Fire_Hydrants + 7: 12 = 0.98 (four marks)10. As runways become contaminated with rain, ice, or snow, aircraft need more time to come to a stop. The James Brake Index (JBI) measures the braking effectiveness of a runway surface. A value of 1 indicates a bare and dry surface, while decreasing numbers imply less effective braking due to contamination. The average stop times measured for six JBI indices are shown. Is it reasonable to conclude that a decrease in JBI causes longer stop times? Give a reason for your answer. 60- 50 40- Stop time_s 30- 10- 0.0 0.2 0.4 0.6 0.8 1.0 1.2 James_Brake_Index Stop_time_s = -38.8James_Brake_Index + 62.5; r2 = 0.97 (four marks)11. As runways become contaminated with rain, ice, or snow, aircraft need more time to come to a stop. The James Brake Index (JBI) measures the braking effectiveness of a runway surface. A value of 1 indicates a bare and dry surface, while decreasing numbers imply less effective braking due to contamination. The average stop times measured for six JBI indices are shown. What stop time would be expected for a JBI of 0.1? (four marks) MDM4U Lesson Assignment Page 10
