Download English 9

Probability and
Statistics
Lesson Activities
Interpreting the Shape of Data Distributions
The Lesson Activities will help you meet these educational goals:
 Mathematical Practices—You will make sense of problems and solve them, reason
abstractly and quantitatively, and use mathematics to model real-world situations.
 Inquiry—You will analyze results and draw conclusions.
 STEM—You will apply mathematical and technology tools and knowledge to analyze
real-world situations.
 21st Century Skills—You will employ online tools for research and analysis.
Directions
You will evaluate some of these activities yourself, and your teacher may evaluate others.
Please save this document before beginning the lesson and keep the document open for
reference during the lesson. Type your answers directly in this document for all activities.
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Self-Checked Activities
Read the instructions for the following activities and type in your responses. At the end of the
lesson, click the link to open the Student Answer Sheet. Use the answers or sample
responses to evaluate your own work.
1. Wages on the Job
While deciding whether to get a job or to continue your education, you consider two small,
local companies that are hiring: KwikFix and MongoRama. You learn that both employers
consider you to be on par with their average worker.
You do some research on the hourly wage each company pays. You find that
MongoRama pays nine employees $9.00 per hour each, while one employee makes
$30.00 per hour. KwikFix pays two employees $9.00 per hour, five employees $10.50 per
hour, two employees $12.00 per hour, and one employee $16.50 per hour.
a. Calculate the mean and the median for the salaries of the two companies, each of
which has 10 employees.
Type your response here:
b. If you were offered a job by both companies, which measure (mean or median) would
you focus on when deciding which offer to accept? Why did you choose this measure?
Type your response here:
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c. Looking at the salary distribution, which company would you choose to work for (all
other employment conditions being the same)?
Type your response here:
d. Write a paragraph explaining the reason for your choice of company.
Type your response here:
How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.
Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.
2. Income and Amount of Education
You’ve chosen between the two companies and have started working at KwikFix. You find
yourself enjoying some of the tasks you do and would like to explore the possibility of
grooming yourself for careers that involve these kinds of tasks. Some of these careers
require a two-year associate’s degree, while others require a bachelor’s degree or even a
graduate or a professional degree.
Open this spreadsheet and select the tab labeled Income by Education (%). Pay close
attention to the findings in the columns labeled Median income (current dollars) and Mean
income (current dollars) in relation to the level of education completed.
a. What general conclusions can be drawn when you compare salaries with education
levels? (Note that professional degrees—such as those for doctors and lawyers—
require roughly the same level of education as doctorates, but are focused more
clearly on a particular career emphasis.)
Type your response here:
b. What do you notice about the median and mean incomes for the various education
levels?
Type your response here:
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c. Compare the mean and median incomes for males and females in each educational
category, and note your observations.
Type your response here:
d. What could be the possible reasons for the differences in the median and mean
incomes of males and females in each educational category?
Type your response here:
How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.
Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.
3. Income versus Cost of Post-Secondary Education
After analyzing the data, you decide you’d like to continue your education. Analyze the
data presented in table 4 (page 12) of this document, which lists average costs of
postsecondary schools in the United States.
a. Return to the spreadsheet and select the tab labeled Income by Education ($), which
lists annual income ranges for various educational levels. Find the annual median
incomes required to complete the table.
Type your response here:
Education
Median Annual Income
Some college, no degree
Associate degree
Difference
b. Use table 4 to calculate the cost of tuition and books for a year of schooling. Also
calculate the amount of income you will lose by not working full-time for the 9 months
you are in school. Notes:
 Assume you’re going to a public, in-district, two-year institution, and use the latest
figures.
 For lost income, use median income for those 25 and older. (This amount is for
simplicity only. A person right out of college would likely earn less, so this cost
calculation will be a little higher than reality.)
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
Finally, since you would have room and board expenses whether you were in
school or working, we won’t include it in this cost comparison.
Type your response here:
Calculation
tuition and books for the second year
lost income by not working full-time for 9
months while in college
total cost of second year of college
c. How many years after graduation will it take you to recover your investment in your
education?
Type your response here:
Calculation
total expenses to be recovered
income difference after graduation
time to recover expenses after graduation
d. Assuming a 40-year career after graduation, what is the difference in your lifetime
earnings? Explain which career path seems more lucrative.
Type your response here:
Calculation
career years remaining after recovering
added education costs
earnings over this period with an associate
degree
earnings over this period with some college
(no degree)
lifetime difference
e. Beyond this financial difference, how might more education provide greater security for
you as you continue to work throughout your lifetime?
Type your response here:
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How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.
Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.
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