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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. _________________________________________________________________________ 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: Copyright © 2012 PLATO Learning, Inc. All rights reserved. 1 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: 2 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.) 3 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: 4 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. 5