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4.4 Assignment: Data management
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Instructions
There are 4 Tasks in this assessment opportunity
Task 1: Knowledge and Understanding
Show all work for each question.
- Would you use primary or secondary data in each situation?
- To determine the percentage of fellow workers who drink at least one coffee a day. (2 marks)
- To find the average weight of Canadian (2 marks)
- 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.
- What was the median number of tickets given out on any particular day in the month of March? (2 marks)
- 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)
- A test has a maximum possible score of 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)
- Imagine that the Consumer Price Index for Canada in 2020 was 6. Assume a base year was established in 2006.
- What can you conclude about prices in Canada in 2020? (1 mark)
- If a set of tires cost $440 in 2006, how much would the same set of tires cost(approximately) in 2020? (4 marks)
- Calculate the body mass index (BMI) of a person who is 5’1” and 120 (Round to one decimal place.) (3 marks)
- Given the correlation coefficient (r-value), determine the strength of the Defend your answers. (6 marks)
- r = −1
- r = 86
- r = −0.12
Task 2: Applications
Show all work for each question.
- 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 |
- Draw a scatter plot, without using graphing (3 marks)
- Draw the line of best (1 mark)
- Determine the slope of your line of best fit and identify the y-intercept. (3 marks)
- Determine the equation of the line of best fit without technology (2 marks)
- Draw a scatter plot using (2 marks)
- Determine the equation of the line of best fit using technology (2 marks)
- Draw the line of best (1 mark)
- 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)
- Your maximum heart rate depends on your These data were collected from a sports journal:
|
Age (years) |
20 |
25 |
30 |
|
Maximum heart rate (beats/min) |
206 |
200 |
194 |
- Draw a scatter plot of the Find the equation of the line of best fit. (3 marks)
- Determine the correlation How well does the line fit the data? (3 marks)
- 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.
- Given the graph of the distribution of fouls received by each player on a basketball team,
|
Number of fouls |
Frequency |
|
1 |
2 |
|
2 |
3 |
|
3 |
3 |
|
4 |
0 |
|
5 |
2 |
- Determine if the distribution represents one- or two-variable data? (1 mark)
- Formulate two questions about the set of (2 marks)
- Identify the population in each of the following data collection scenarios
- A school wants to know what type of music to play at the next Grade 8 (1 mark)
- The Ministry of Education wants to know how people feel about the course they have taken. (1 mark)
- When graphing one-variable data, is the frequency the dependent or the independent variable? (1 mark)
- A survey asks the question, “What is your favourite colour: red or black?” State whether this is a valid question for determining favourite Which three words should be deleted to make the question better? (2 marks)
- State whether the following results are both reliable and Explain. (6 marks)
- 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.
- All the traffic lights in a town are timed and it is found that they consistently stay yellow for four seconds.
- 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
- Determine if the following scenarios would have a cause-and-effect Explain. (6 marks)
- Toronto’s temperature goes up and then the world stock market prices go up the same day.
- The student’s hours of studying and practising for tests and the student’s score on tests.
- Explain how to interpret the value of the correlation (2 marks)
- A math teacher introduces a mathematics game to 20 Grade 12 students in order toteach a new 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.
- Given the graph,
|
Age |
Height |
|
1 |
2 |
|
2 |
3 |
|
3 |
4 |
|
4 |
5 |
|
5 |
6 |
|
6 |
7 |
- Describe any trends you (2 marks)
- Why is this graph limited in its effectiveness and how could it be improved? (2 marks)
- The following graph is meant to display a relationship between the amounts of snowfallen Toronto over a period of 10 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)
- 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 The years have not been provided as you will only need the amounts.
|
Sales ($) (thousands) |
Profit ($) (thousands) |
|
195 |
10 |
|
205 |
15 |
|
225 |
22 |
|
4240 |
−10 |
|
255 |
25 |
|
300 |
39 |
|
265 |
25 |
|
345 |
55 |
|
295 |
32 |
|
335 |
37 |
|
380 |
48 |
|
Sales ($) (thousands) |
Profit ($) (thousands) |
|
405 |
55 |
|
355 |
50 |
|
390 |
48 |
|
410 |
55 |
- Enter the data from the table into a spreadsheet Include the headings for the two columns. (3 marks)
- Sort the data from smallest to largest in the sales (2 marks)
- In an empty cell below the profit column, show the sum of the profit (1 mark)
- Create a scatter plot for this (2 marks)
NOTE: This solution should have separate screenshots of the spreadsheet for parts a. and b.
- 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 |
- Create a scatter (3 marks)
- Determine the correlation (2 marks)
- Describe the type of relation and the strength of the (2 marks)
- Does the age of a gym member affect the number of hours that a member exercises per week? (2 marks)
- How reliable and valid do you think the information is? (2 marks)
Assessment Requirements (Brief Summary)
This assessment was divided into four major tasks designed to test the learner’s knowledge, application, communication, and thinking skills within the context of mathematics, statistics, and data interpretation.
-
Task 1: Knowledge and Understanding
Focused on identifying primary vs. secondary data, calculating measures such as median, quartiles, percentiles, interpreting Consumer Price Index (CPI), Body Mass Index (BMI), and correlation coefficients. -
Task 2: Applications
Required plotting and analyzing scatter plots, drawing lines of best fit (manually and with technology), determining equations, predicting outcomes, and interpreting real-world datasets like exchange rates and heart rates. -
Task 3: Communication
Tested the ability to interpret and explain data scenarios, identify valid survey questions, determine populations, discuss reliability and validity of results, and explain cause-and-effect or correlation relationships. -
Task 4: Thinking
Involved analyzing graphs for trends, identifying misleading presentations, using spreadsheets for sorting, summation, and scatter plotting, and interpreting correlation between variables like age, sales, and exercise hours.
Overall, the assessment aimed to evaluate analytical skills, logical reasoning, mathematical calculations, statistical communication, and application of technology in data handling.
Mentor’s Step-by-Step Guidance Approach
The Academic Mentor guided the student systematically through each section, ensuring clarity of concepts, accuracy of methods, and application of logical reasoning.
Step 1: Understanding Task 1 – Knowledge and Understanding
-
The mentor first explained primary vs. secondary data with real-life examples to ensure the student could correctly classify scenarios.
-
For calculations like median, quartiles, and percentiles, the mentor broke the dataset into ordered values and demonstrated the step-by-step process.
-
For CPI and inflation calculations, the mentor guided the student in applying index formulas to calculate adjusted prices.
-
For BMI, the mentor ensured unit conversion before applying the formula.
-
While interpreting correlation coefficients, the mentor provided context (perfect positive, perfect negative, weak correlation) so the student could defend each answer logically.
Step 2: Tackling Task 2 – Applications
-
The mentor emphasized manual plotting first to build conceptual clarity before moving to technology-based plotting.
-
The slope, y-intercept, and equations of best fit were derived step-by-step with clear formulas.
-
The student was then guided to cross-verify results with technological tools, ensuring they understood differences in accuracy.
-
Predictions, such as exchange rate forecasts, were explained in terms of real-world implications and reliability.
-
For the heart rate dataset, the mentor helped the student connect regression results with biological plausibility, reinforcing critical thinking.
Step 3: Addressing Task 3 – Communication
-
The mentor encouraged the student to differentiate one-variable vs. two-variable data clearly.
-
Together, they rephrased invalid survey questions to demonstrate how wording impacts research reliability.
-
The mentor guided the student in identifying valid populations in scenarios, emphasizing inclusivity and accuracy.
-
Reliability and validity of surveys were discussed with examples, helping the student argue strengths and weaknesses in reasoning.
-
Cause-and-effect vs. correlation scenarios were explained with real-life analogies to avoid misconceptions.
Step 4: Solving Task 4 – Thinking
-
For identifying trends in graphs, the mentor highlighted the importance of recognizing both limitations and improvements in representation.
-
Misleading graphs were analyzed critically to spot distortions (e.g., manipulated scales).
-
The student was guided through spreadsheet functions (sorting, summation, plotting), ensuring hands-on familiarity with digital tools.
-
In correlation exercises, the mentor explained how to calculate correlation coefficients and interpret their meaning regarding strength and reliability.
-
Finally, reliability and validity discussions were reinforced by comparing real datasets to hypothetical ones.
Outcome and Learning Objectives Achieved
Through this structured approach, the student:
-
Developed strong statistical skills in calculating, analyzing, and interpreting datasets.
-
Understood the role of primary vs. secondary data and when each should be applied.
-
Applied mathematical reasoning to real-life contexts (CPI, BMI, heart rates, exchange rates).
-
Built communication skills by explaining findings clearly, identifying populations, and evaluating data validity.
-
Enhanced critical thinking by questioning misleading information and interpreting data relationships responsibly.
-
Gained technical competence in using spreadsheets for sorting, summation, and graphical representation.
-
Achieved holistic understanding by linking theory, practice, and technology in solving assessment tasks.
The assessment outcome demonstrated not only accuracy in calculations but also clear reasoning, critical interpretation, and reflective communication, aligning with all intended learning objectives.
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