4.4 Assignment_ Data management

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Sir William Mulock Secondary School *

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MCV4U

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Statistics

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Jun 24, 2024

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4.4 Assignment: Data management This is an assessment opportunity which is used to evaluate your work based on established criteria. Instructions There are 4 Tasks in this assessment opportunity Task 1: Knowledge and Understanding Show all work for each question. 1. Would you use primary or secondary data in each situation? Explain. a. To determine the percentage of fellow workers who drink at least one coffee a day. (2 marks) b. To find the average weight of Canadian men. (2 marks) 2. For each day in the month of March, the number of cars given speeding tickets was as follows: 56, 57, 43, 56, 87, 37, 76, 55, 29, 65, 84, 74, 46, 58, 61, 40, 43, 60, 51, 77, 53, 47, 50, 81, 61, 44, 55, 54, 76, 39, and 77. a. What was the median number of tickets given out on any particular day in the month of March? (2 marks) b. If your friend was caught speeding on a day when only 43 tickets were awarded, does the day rank below the lower quartile? (3 marks) 3. A test has a maximum possible score of 200. The results achieved by a class of 20 students are listed: 168, 152, 112, 88, 95, 123, 177, 166, 145, 104, 112, 156, 110, 141, 177, 166, 134, 190, 111, and 120. Calculate the percentile rank of a score of 141, to the nearest percentile. (4 marks) 4. Imagine that the Consumer Price Index for Canada in 2020 was 102.6. Assume a base year was established in 2006. a. What can you conclude about prices in Canada in 2020? (1 mark) b. If a set of tires cost $440 in 2006, how much would the same set of tires cost(approximately) in 2020? (4 marks) 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 1/8

5. Calculate the body mass index (BMI) of a person who is 5’1” and 120 lb. (Round to one decimal place.) (3 marks) 6. Given the correlation coefficient (r-value), determine the strength of the relationship. Defend your answers. (6 marks) a. r = −1 b. r = 0.86 c. r = −0.12 Task 2: Applications Show all work for each question. 7. The average annual exchange rate in Canada for the US dollar from 2008-2018 is shown in the following table. Year Exchange rate 2008 0.94 2009 0.88 2010 0.97 2011 1.01 2012 1.00 2013 0.97 2014 0.91 2015 0.78 2016 0.77 2017 0.77 2018 0.77 a. Draw a scatter plot, without using graphing technology. (3 marks) b. Draw the line of best fit. (1 mark) c. Determine the slope of your line of best fit and identify the y-intercept. (3 marks) 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 2/8

d. Determine the equation of the line of best fit without technology (2 marks) e. Draw a scatter plot using technology. (2 marks) f. Determine the equation of the line of best fit using technology (2 marks) g. Draw the line of best fit. (1 mark) h. Based on your findings (use both equations of the line of best fit), what will the average exchange rate be in the year 2020, if current trends continue? Which one do you think is the most accurate? Why? (4 marks) 8. Your maximum heart rate depends on your age. These data were collected from a sports journal: Age (years) 20 25 30 Maximum heart rate (beats/min) 206 200 194 a. Draw a scatter plot of the data. Find the equation of the line of best fit. (3 marks) b. Determine the correlation coefficient. How well does the line fit the data? (3 marks) c. Use the equation to give a prediction of the maximum heart rate for a person of 23 years? (1 mark) Task 3: Communication Show all work for each question. 9. Given the graph of the distribution of fouls received by each player on a basketball team, 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 3/8

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Number of fouls Frequency 1 2 2 3 3 3 4 0 5 2 a. Determine if the distribution represents one- or two-variable data? (1 mark) b. Formulate two questions about the set of data. (2 marks) 10. Identify the population in each of the following data collection scenarios a. A school wants to know what type of music to play at the next Grade 8 dance. (1 mark) b. The Ministry of Education wants to know how people feel about the course they have taken. (1 mark) 11. When graphing one-variable data, is the frequency the dependent or the independent variable? (1 mark) 12. A survey asks the question, “What is your favourite colour: red or black?” State whether this is a valid question for determining favourite colours. Which three words should be deleted to make the question better? (2 marks) 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 4/8

13. State whether the following results are both reliable and valid. Explain. (6 marks) a. A national political survey asks a group of high school students what party they favour in order to determine which party will win the next election. b. All the traffic lights in a town are timed and it is found that they consistently stay yellow for four seconds. c. The radio station Fan 590 has a phone-in survey to determine if the coach of the Toronto Maple Leafs should be fired and 93% of the people who call in are in favour. 14. Determine if the following scenarios would have a cause-and-effect relationship. Explain. (6 marks) a. Toronto’s temperature goes up and then the world stock market prices go up the same day. b. The student’s hours of studying and practising for tests and the student’s score on tests. 15. Explain how to interpret the value of the correlation coefficient. (2 marks) 16. A math teacher introduces a mathematics game to 20 Grade 12 students in order toteach a new concept. The teacher finds a positive correlation between the use of the game and the mastering of the concept. The teacher concludes that the game would teach the concept toall students in high school. Discuss whether the conclusion is valid or not. (3 marks) Task 4: Thinking Show all work for each question. 17. Given the graph, 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 5/8

Age Height 1 2 2 3 3 4 4 5 5 6 6 7 a. Describe any trends you see. (2 marks) b. Why is this graph limited in its effectiveness and how could it be improved? (2 marks) 18. The following graph is meant to display a relationship between the amounts of snowfallen Toronto over a period of 10 years. Assume that the data points are correct. Examine the graph and answer the question: How does the following graph present information in a way that is misleading or distorted? (2 marks) 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 6/8

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Press here for a long description. (../alt/map4c_04.04.27.html?ou=25315776) 19. The information in the following table shows the amount of sales and the profit from a small retail business in Whitby Ontario for the last 15 years. The years have not been provided as you will only need the amounts. Sales ($) (thousands) Profit ($) (thousands) 195 10 205 15 225 22 4240 −10 255 25 300 39 265 25 345 55 295 32 335 37 380 48 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 7/8

Sales ($) (thousands) Profit ($) (thousands) 405 55 355 50 390 48 410 55 a. Enter the data from the table into a spreadsheet program. Include the headings for the two columns. (3 marks) b. Sort the data from smallest to largest in the sales column. (2 marks) c. In an empty cell below the profit column, show the sum of the profit column. (1 mark) d. Create a scatter plot for this data. (2 marks) NOTE: This solution should have separate screenshots of the spreadsheet for parts a. and b. 20. The following information on age and number of hours exercised was gathered about 13 members at a small gym. Age 25 36 44 22 57 25 43 19 33 40 44 28 25 Hours 6 5 4 6.5 2 5 4 7 4.5 3 2.5 6.5 5.5 a. Create a scatter plot. (3 marks) b. Determine the correlation coefficient. (2 marks) c. Describe the type of relation and the strength of the relation. (2 marks) d. Does the age of a gym member affect the number of hours that a member exercises per week? (2 marks) e. How reliable and valid do you think the information is? (2 marks) 6/15/24, 1:45 PM 4.4 Assignment: Data management https://course.ilc.tvo.org/content/enforced/25315776-MAP4C-EN-02-0324-ON-(I-D)/course_content/assets/locker_docs/map4c_04.04.100.html?ou=25315776 8/8

4.4 Assignment_ Data management

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