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# Descriptive Statistics in the NCAA

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A Webquest activity for a high school statistics class.

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### Descriptive Statistics in the NCAA

1. 1. Descriptive Statistics of the NCAA Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] A WebQuest for 11th Grade Statistics Designed by Susan Thomas [email_address] Based on a template from The WebQuest Page
2. 2. Introduction Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] This assignment is an investigation into descriptive statistics. We have all heard the about sports stats and hopefully know that that it refers to sports statistics. In this assignment, you will take find sports statistics online and turn then into descriptive statistics which will then be analyzed. I have chosen men’s college basketball, specifically the Big 10 Conference, in honor of March Madness. The goal is to use descriptive statistics to summarize the team’s performance throughout the season. How many points did a team average? What was their point differential? How many wins/successes? There are all sorts of sports stats that can be summarized by descriptive statistics, and analyzed using hypothesis tests and confidence intervals. Now that you know the basics of descriptive statistics, apply them on some real-life data.
3. 3. The Task Student Page Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] <ul><li>Now that the competition is really on for the NCAA basketball tournament, let’s find out how some of the teams performed in the regular season and how that may have helped predict their final ranking and success. Pick your favorite 2-4 Big 10 teams and take on one of the roles. You will participate in statistics by: </li></ul><ul><ul><li>locating data on current basketball teams; </li></ul></ul><ul><ul><li>determining which statistics you think are most important to analyze; </li></ul></ul><ul><ul><li>calculating descriptive statistics and conducting tests based on the teams’ performance; </li></ul></ul><ul><ul><li>creating useful visual representations of the data; </li></ul></ul><ul><ul><li>translating statistical results into common language. </li></ul></ul><ul><li>Once you can do all this, I will know you have mastered descriptive, and you will learn a use for them. You will display this knowledge and skill in a final project on PowerPoint that will be presented to the class. </li></ul><ul><li>Things to keep in mind that you have learned: </li></ul><ul><li>sample, population, population mean, population median, sample variance, standard deviation, interquartile range, lower/upper quartile, outliers, confidence intervals, z-tests, histograms, and box plots </li></ul><ul><li>You will use the following websites to retrieve data: </li></ul><ul><li>www.uiuc.edu/ , www.indiana.edu/ , www.uiowa.edu ,www.umich.edu / , www.msu.edu/ , www.umn.edu/ , www.northwestern.edu/ , www.osu.edu/ , www.psu.edu/ , www.purdue.edu/ , www.wisc.edu/ </li></ul>Title
4. 4. The Process Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] <ul><li>To accomplish this task, here are the steps every group must follow: </li></ul><ul><li>First you'll be assigned to a team of 4 students. </li></ul><ul><li>After groups have been established, each team member should choose a role. </li></ul><ul><li>Each team member should have something to start on to get the project started. Everyone should have some preliminary research for their task. </li></ul><ul><li>After the data is retrieved, start calculating your statistics. At the same time, others will work on linking real life meaning to statistical meaning. </li></ul><ul><li>With data analyzed, work on presentation including layout of presentation or results and the creation of graphs, charts, and other visuals. </li></ul><ul><li>Students should finish with putting all the parts together and editing as a group. </li></ul><ul><li>Now that you know what your game plan is, choose a role that suits you and fits in with the group’s needs. Choose wisely, because your group members are counting on you to do your best. Here are the roles that members of the group must play: </li></ul><ul><li>researcher </li></ul><ul><li>statistics specialist </li></ul><ul><li>number cruncher </li></ul><ul><li>graphics designer </li></ul><ul><li>The researcher will be in charge of choosing the schools whose team will be analyzed. They also must identify the population and sample being studied and create a written description of them. </li></ul><ul><li>The statistics specialist will decide the relevant data and help the researcher retrieve them. They will also determine which tests to perform and what their conclusions will mean. </li></ul><ul><li>The number cruncher will be in charge of calculating the descriptive statistics including mean, median, IQR, standard deviation, variance, and t-tests. </li></ul><ul><li>The graphics designer will be responsible for creating visual representations of the results in the form of tables, graphs, histograms, etc. </li></ul>
5. 5. Evaluation: Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Math - Problem Solving : Descriptive Statistics of the NCAA           Teacher Name: Susan Thomas Student Name:     ________________________________________ CATEGORY 4 3 2 1 Mathematical Reasoning Uses complex and refined mathematical reasoning. Uses effective mathematical reasoning Some evidence of mathematical reasoning. Little evidence of mathematical reasoning. Neatness and Organization The work is presented in a neat, clear, organized fashion that is easy to read. The work is presented in a neat and organized fashion that is usually easy to read. The work is presented in an organized fashion but may be hard to read at times. The work appears sloppy and unorganized. It is hard to know what information goes together. Diagrams and Sketches Diagrams and/or sketches are clear and greatly add to the reader's understanding of the procedure(s). Diagrams and/or sketches are clear and easy to understand. Diagrams and/or sketches are somewhat difficult to understand. Diagrams and/or sketches are difficult to understand or are not used. Mathematical Terminology and Notation Correct terminology and notation are always used, making it easy to understand what was done. Correct terminology and notation are usually used, making it fairly easy to understand what was done. Correct terminology and notation are used, but it is sometimes not easy to understand what was done. There is little use, or a lot of inappropriate use, of terminology and notation. Completion All problems are completed. All but 1 of the problems are completed. All but 2 of the problems are completed. Several of the problems are not completed. Date Created: Mar 24, 2008 12:05 pm (CDT)
6. 6. Conclusion Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Congratulations! This is probably the first time you have applied your knowledge from statistics to real world data. Hopefully the concepts of descriptive statistics mean a little more to you now and will stay in your memory for a little while. Who knows, maybe you even enjoyed it (deep down you did) and will have the interest to calculate more statistics. What other scenarios could you find similar information and conclusions for, and how could you use it?
7. 7. Credits & References Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Basketball picture on Title page posted on flickr.com by Scuddy on May 14, 2007. Photo on Introduction slide titled UWP Men’s BBall2 posted on flickr.com by Kevin Poirier on January 21, 2008. Links found based on list of Big 10 schools at http://bigten.cstv.com/. Original link where template is located is to The WebQuest Page and The WebQuest Slideshare Group where others can acquire the latest version of this template and training materials.
8. 8. Descriptive Statistics of the NCAA (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page A WebQuest for 11th Grade Statistics Designed by Susan Thomas [email_address] Based on a template from The WebQuest Page Evaluation Teacher Script Conclusion
9. 9. Introduction (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page This project was designed to meet the Colorado Mathematical Standards provided by the Colorado Department of Education at www.cde.state.co.us/coloradomath/Standards_and_Assessment.htm . Specifically, it is geared towards standard 3, which is for students to use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems. For specific benchmarks for grades 9-12, this project meets those for designing and conduct a statistical experiment to study a problem, and interpret and communicate the results using the appropriate technology and drawing conclusions about distributions of data based on analysis of statistical summaries. This lesson is sort of a final project for a unit on descriptive statistics and confidence intervals and t-tests. It will require students to find statistics on their own, with no known right or wrong answer, and to translate their statistical data into something that makes sense to them in the real world. Evaluation Teacher Script Conclusion
10. 10. Learners (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page The grade level will vary depending on the school and the curriculum. In general, this project will be good for an Advanced Placement statistics class or standard level statistics class, which would typically be taken in 11 th or 12 th grade. It may also fit in with some other integrated curriculums with a different course name, but the same grade level. It involves a lot of basic math, such as addition and multiplication, but more advanced ideas of statistical tests and in-depth descriptions of what results mean. I do not think this would be appropriate for anything prior to 11 th grade. Students are expected to know many specific things. They should know definitions and applications of : sample, population, population mean, population median, sample variance, standard deviation, interquartile range, lower/upper quartile, outliers, confidence intervals, z-tests, histograms, and box plots. They will need to have knowledge of some technology in order to make visuals, which could be a statistical package or excel. The students are also to have written communication skills so that their final project and included summaries make sense to the reader. Evaluation Teacher Script Conclusion
11. 11. Curriculum Standards (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page Students will be learning real world applications of the statistics they have learned so far. They will not just be discovering this, but applying skills they should have. The outcome should be a quality presentation using statistical language and visuals which use accurately calculated summary statistics. Specifically, standards-based skills that are used are data collection and analysis, statistics, and communication of the reasoning used in solving these problems. This lesson will apply to kinesthetic learners and those who learn by discovery. It will also appeal to visual learners who will have the opportunity to express their knowledge through some sort of graphic. It also includes work for the traditional learning styles that excel in writing and math, because there will be plenty of summarizing/explaining as well as calculations. Teamwork and compromise will be involved due to the assignment of roles and reliance on group members. Critical thinking will be important because the results they get are theirs alone, and they will arrive at unique results. Evaluation Teacher Script Conclusion
12. 12. The Process (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page <ul><li>These are the directions given to students: </li></ul><ul><li>First you'll be assigned to a team of 4 students. </li></ul><ul><li>After groups have been established, each team member should choose a role. </li></ul><ul><li>Each team member should have something to start on to get the project started. Everyone should have some preliminary research for their task. </li></ul><ul><li>After the data is retrieved, start calculating your statistics. At the same time, others will work on linking real life meaning to statistical meaning. </li></ul><ul><li>With data analyzed, work on presentation including layout of presentation or results and the creation of graphs, charts, and other visuals. </li></ul><ul><li>Students should finish with putting all the parts together and editing as a group. </li></ul><ul><li>These are the options for roles, and the required tasks: </li></ul><ul><li>researcher - choose the schools, identify the population and sample, write a description, get data. </li></ul><ul><li>statistics specialist- choose statistics, tests, translate conclusions to real world language. </li></ul><ul><li>number cruncher- calculate descriptive statistics (mean,median,IQR,st. dev, variance, t-test) </li></ul><ul><li>graphics designer- create visuals of data, prepare layout. </li></ul><ul><li>This lesson will take several class periods. Step 1,2,3 can be started on day 1 of the lesson. Step 4 and 5 will take another1 or 2 lessons and Step 6 may need a 4 th day, depending on how professional the product is expected to look. </li></ul><ul><li>Since students need to be divided into groups, this should be done strategically. There are various methods of doing this, so it will depend largely on what method has been used for the class so far. Since the 4 roles are fairly different, it would be best to get a variety of learning styles in each group. </li></ul><ul><li>What skills does a teacher need in order to pull this lesson off? Is it easy enough for a novice teacher? Does it require some experience with directing debates or role plays, for example? </li></ul>Evaluation Teacher Script Conclusion
13. 13. Resources (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page <ul><li>Here is what is needed for this lesson: </li></ul><ul><ul><li>Access to computers for at least one out of every group. </li></ul></ul><ul><ul><li>Statistical reference books for each group. </li></ul></ul><ul><ul><li>E-mail accounts for all students so they can share data. </li></ul></ul><ul><ul><li>Some statistical software like SAS or Maple (or Excel at the least) so that at some point each group has access to it. PowerPoint on one computer per group. </li></ul></ul><ul><ul><li>Projection system so that student work can be shown to entire class. </li></ul></ul><ul><li>The data for the NCAA Big 10 Conference can all be accessed through the Big 10 website: http://bigten.cstv.com/ . I provided students with links to the schools though, so they get practice navigating websites and finding their own data, instead of getting it off a list from the Big 10 website. Here is the list of links: </li></ul><ul><li>www.uiuc.edu/,www.indiana.edu/, www.uiowa.edu,www.umich.edu/ , www.msu.edu/,www.umn.edu/, www.northwestern.edu/,www.osu.edu/, www.psu.edu/,www.purdue.edu/ ,www.wisc.edu/ </li></ul><ul><li>If the students are well trained, only one teacher should be necessary. Under ideal conditions, computers will be in the classroom, so the groups will not have to be moved to different rooms and can be supervised by one person. Parents should not be needed, and the computer work is simple enough that high school students can navigate on their own or with the assistance of one teacher. </li></ul>Evaluation Teacher Script Conclusion
14. 14. Evaluation (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page I will know that the lesson was successful if students can find accurate summary statistics on their own, and if their explanations make sense and are consistent with their results. The product should be a group presentation on PowerPoint, or an pdf file if PowerPoint is unavailable. Students will be evaluated on their final product which should be a reflection of their ability to obtain and analyze data and communicate the reasoning involved in the problem solving. Specifically, these are the categories they will be evaluated on and are given in more detail in the rubric : Mathematical Reasoning Neatness and Organization Math Terminology Completion Evaluation Teacher Script Conclusion