NAME: BLOCK: DATE: MATES Statistics: Summer Assignment

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1 MATES Statistics: Summer Assignment This summer assignment is designed to maintain your mathematical skills and to demonstrate mastery of prerequisite topics to the course that you are entering. Collaboration is acceptable and encouraged, but it is important to understand that this assignment is intended to evaluate your individual skill set. If you are having difficulty with the assignment, feel free to speak with other peers or to consult web or written resources. However, please do not consult resources outside of your peer group, i.e. a tutor or your mathematically inclined relative. Statistics is completely different from any other math class you have ever taken. In fact, some would say that it is not a math class at all. Mathematicians have been known to complain that the problem with statistics is that it is not math. At many universities, the math department and the statistics department are distinct. In fact, statistics is applied mathematics, with the addition of skills and concepts unique to statistics, and a large dose of critical thinking and analysis. Please be aware that statistics is a reading and writing course. Almost all problems are word problems how could they be anything else? Statistics is context based what you do depends on the facts. Answers must be complete, which means your analysis and choice of method explained in sentences, followed by your calculations. Note that although you have the entire summer to complete the assignment, you may not be able to complete it in one sitting. Start early and allow yourself time to seek help per the guidelines above. This assignment can also be accessed from the OCVTS website at follow the link for the MATES page. This assignment will be collected on the first day of school. Late assignments will not be accepted. Please read and follow all directions carefully. This is your first opportunity to demonstrate your work ethic to the instructor. It will count as your first assessment grade. Good luck! Sincerely, MATES Math Department 1

2 VIDEO URL: Go to the URL listed above and watch the following videos. Take out a piece of paper and be ready to write down answers to these questions as you watch the video. 1. What is Statistics? 2. Stemplots 1. List some of the variables that were taken on soldiers for the sizing data bank. 2. What was the overall shape of the distribution of soldiers foot lengths? About where was the center of the distribution? 3. What variable was used to measure fuel economy on Toyota s line of vehicles? 4. Focus on the stemplot of fuel economy for Toyota s 2012 line. What new information became evident (or clearer) when the stem was expanded? 5. What was learned from back-to-back stemplots about the change in fuel economy in Toyota s vehicle line from 1984 to 2012? 2

3 Exercises: You may use calculator or spreadsheet technology for the exercises, but please explain how you are obtaining your results. 1. The video mentioned the fact that soldiers are bulking up along with the rest of America. Even so, soldiers are expected to be physically fit. Suggest several quantitative variables that you might use to measure fitness. Keep in mind that each of your variables must produce a number that represents fitness. 2. Below are the number of home runs that Babe Ruth hit in each of his 15 years with the New York Yankees, a) Make a stemplot of the home run data. Then use your stemplot to answer questions (b) and (c). b) Describe the shape of the distribution. Is it roughly symmetric or not? Is it unimodal (single peak) or multimodal (more than one peak)? c) What is the center (this is the number of home runs the Babe hit in a typical year)? 3

4 d) Ruth s record of 60 home runs in 1927 stood for more than 30 years. Is 60 an observation that falls outside the pattern of the other observations and hence could be considered an outlier? 3. The SAT is a standardized test for college admissions that is widely used in the United States. The table below contains the average score for each state on the Critical Reading, Math, and Writing sections of the SAT for Mean 2011 SAT Scores by State. States are listed by total 2011 SAT Scores. Rank State Critical Reading Math Writing Participation Combined Rate. 1 Illinois %. 2 Minnesota %. 3 Iowa %. 4 Wisconsin %. 5 Missouri %. 6 Michigan %. 7 North Dakota %. 8 Kansas %. 9 Nebraska %. 10 South Dakota %. 11 Kentucky %. 12 Tennessee %. 13 Colorado %. 14 Wyoming %. 15 Arkansas %. 16 Oklahoma %. 17 Utah %. 18 Mississippi %. 19 Louisiana %. 20 Alabama %. 21 New Mexico %. 22 Ohio %. 23 Idaho %. 24 Montana %. 25 Washington %. 26 New Hampshire %. 27 Massachusetts %. 28 Oregon % 4

5 . 29 Arizona %. 30 Vermont %. 31 Connecticut %. 32 Virginia %. 33 California %. 34 Alaska %. 35 West Virginia %. 36 New Jersey %. 37 Maryland %. 38 Rhode Island %. 39 North Carolina %. 40 Pennsylvania %. 41 Indiana %. 42 New York %. 43 Nevada %. 44 Delaware %. 45 Hawaii %. 46 Florida %. 47 Texas %. 48 Georgia %. 49 South Carolina %. 50 Maine % District of Columbia % Source: College Board a) Complete the following table. Describe your methods of calculation. Description Result How did you compute this result? State with highest Critical Reading Score State with lowest Critical Reading Score Mean Critical Reading Score Average Participation Rate (round to nearest tenth) Average Combined Score (round to nearest tenth) State with highest Math Score State with lowest Math Score Mean Math Score 5

6 b) Make a stemplot of the 51 average SAT Critical Reading scores. Use a separate sheet of paper. c) Based on your stemplot, describe the overall shape of the distribution of SAT Critical Reading scores. Approximate the center. Are there any outliers? d) Make a back-to-back stemplot of the SAT Math and SAT Writing scores. Use a separate sheet of paper. e) Based on your stemplot, compare the distributions of the SAT Math and SAT Writing scores. Compare shape, center, and spread. 4. Browse the other videos listed on the web page above. Choose one that interests you and watch it. VIDEO: After watching the video, use a word processor to prepare responses to the following questions. Include a copy of your response as a separate attachment. a) What were the main ideas presented in this video? b) Describe something new that you learned in a detailed paragraph. Were there any new mathematical concepts or definitions presented? c) What are some of the practical applications for the concepts that were presented in the video? 6