hign school math MATHEMATICS OF DATA MANAGEMENT

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

4. All answers must be written in pencil, black or blue pen.

5. Student should not have any electronic gadget on them during the examination

6. Student should bring along their calculators

Good Luck!

SECTION A 28 marks

Knowledge and understanding

1. 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

a. Create a frequency distribution table for the data

b. Determine the mean, median, and mode of the temperatures.

c. Determine the variance and standard deviation for the temperatures

d. Create a box and whisker plot of the data

e. Determine the outlier if any

f. Which measure of central tendency would best represent the temperatures in New York? Explain.

2. 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

3. 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?

4. 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

5. 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

6. With a specific example, explain how an outlier can affect the measures of central tendencies

7. Compare measures of spread and measures of the central tendencies

SECTION D 18 marks

Thinking / Inquiry

8. 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?

9. 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.

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