MDM4U Mathematics of Data Management Essay
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MDM4U Mathematics of Data Management Essay
Course Code: MDM4U
FINAL EXAMINATION
Due: December 17th, 2021
Time: 1:00 p.m. EST
Student Name: _______________________________________ _______
Please read the following instructions carefully before you begin the examination:
The examination is worth thirty percent (30%) of your final mark.
The examination consists of three (4) sections.
SECTION CONTENT MARKS Student’s Mark A Knowledge / Understanding) (25%) 28 Marks B Application (25%) 12 Marks C Communication (25%) 9 Marks D Thinking / Inquiry (25%) 18 Marks TOTAL 70
- All answers must be written in pencil, black or blue pen.
- Student should not have any electronic gadget on them during the examination
- Student should bring along their calculators
Good Luck!
SECTION A 28 marks Knowledge and understanding
- Regina spent the first seven days of her holidays in New York, USA. She recorded the temperatures for seven days as follows: 5, 10, 14, 12, 8, 10, and 11
- Create a frequency distribution table for the data
- Determine the mean, median, and mode of the temperatures.
- Determine the variance and standard deviation for the temperatures
- Create a box and whisker plot of the data
- Determine the outlier if any
- Which measure of central tendency would best represent the temperatures in New York? Explain.
- A teacher is calculating the marks for the students in her Data Management class. She assigns the following values to each category:
Knowledge: 25%, Thinking: 20%, Application: 20%, Communication: 20%, and final examination 15%.
Angel has not yet written her final examination, but her marks in the first four categories are 90, 60, 75, and 70.
- a) Determine the weighted mean for Angel before the final exam.
- b) Determine the unweighted mean for Angel before the final exam
- c) What mark must Angel receive on the final exam to finish the course with 75%?
SECTION B 12 marks Application
- A nuclear plant in Ontario releases some radioactive substances into the air. For example, a 100-MW coal plant releases a mean of 500 kg of uranium per year, with a standard deviation of 120 kg. The release of uranium follows a normal distribution.
- a) What is the probability that the plant will release less than 450 kg of uranium in a given year?
- b) What is the probability that the plant will release more than 450 kg of uranium in a given year?
- c) What is the probability that the release will be within 5% of the mean?
- During the covid-19 pandemic, a survey of small businesses in the Greater Toronto Area showed that a mean of 10% of gross income was spent on protective supplies, with a standard deviation of 2%, following a normal distribution. At a 95% confidence level, the margin of error was 8%. How many businesses were surveyed?
SECTION C 9 marks Communication
- You were contracted to conduct research for a bank in Ontario. You found the upper and lower limits of a 95% confidence interval to be 12 g and 20g respectively. Explain the meaning of your result to the clients
- With a specific example, explain how an outlier can affect the measures of central tendencies
- Compare measures of spread and measures of the central tendencies
SECTION D 18 marks Thinking / Inquiry
- The table shows distance from home for a cyclist over time.
Time (min) Distance (km) 5 3 10 3.6 15 4.7 20 10 25 6.5
- a) Create a scatter plot relating distance, d, and time, t.
Note: Plot distance (d), on the y-axis and time (t) on the x-axis.
- b) Show the trend on your scatter plot.
- c) Determine the strength of linear correlation.
- d) Determine the equation of the line of best fit and explain what it means.
- e) Why do the actual data points not always fall exactly on the line?
- A set of five whole numbers is arranged in order from least to greatest. The fifth number is decreased by one. Would the interquartile range or standard deviation be more affected? Explain.
RUBRIC
Excellent Quality
95-100%
Introduction 45-41 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Literature Support
91-84 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Methodology
58-53 points
Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score
50-85%
40-38 points
More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points
Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points
Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality
0-45%
37-1 points
The background and/or significance are missing. No search history information is provided.
75-1 points
Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.
48-1 points
There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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