What Should Your Salary Be? Using Statistical Graphs to Compare Data - Grade 10

Transcription

1 Content Standards: Data Analysis and Probability What Should Your Salary Be? Using Statistical Graphs to Compare Data - Grade 10 Benchmark A Create, interpret and use graphical displays and statistical measures to describe data; e.g., boxand-whisker plots, histograms, scatterplots, measures of center and variability. Indicator 6 Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread. Benchmark D Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data. Indicator 6 Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread. Mathematical Processes Benchmarks A. Formulate a problem or mathematical model in response to a specific need or situation, and determine information required to solve the problem, to choose a method for obtaining this information, and to set limits for acceptable solution. E. Use a variety of mathematical representations flexibly and appropriately to organize, record, and communicate mathematical ideas. Pre-Assessment: (optional) Activity: Basketball Data, Attachment A. First, use technology to create the histograms and box-and-whisker plots needed in Basketball Data, Attachment A; Students work in groups, to create the statistical graphs needed for the rest of the lesson; As the students work together, circulate to be sure that they can create the graphs, providing individual help when needed; If many students are unable to complete the task, review entering data and creating histograms and box-and-whisker plots. Instructional Tip: When the students enter the data into calculator lists, the data is displayed in scientific notation. Students may need to be reminded about the calculator form of scientific notation; (e.g., 3,120,000 is displayed as 3.12E6). However, numbers are displayed in standard form when students trace on the box-and-whisker plot.

2 Scoring Guideline: Informal assessment will be completed by teacher observation to determine that students can complete the graphs. Post-Assessment: Which Basketball Team Shall I Sign With?? (Attachment B) Each group analyzes two new sets of data by making graphs. All students submit reports of their conclusions and close with comparison discussion of the findings. Instructional Tip: If the students complete the exercise on the computer, they may prepare their reports on the computer and submit them either as hard copies or electronically. If they complete the exercise on calculators and have access to computers and the technology to link the graphing calculator to the computer, they may complete their reports using word processors, inserting the calculator graphs at the appropriate places in the report. These may also be submitted as hard copy or electronically. Scoring Guidelines: The report will be graded with the Analytic Rubric, Attachment C. Instructional Procedures: 1. Complete the pre-assessment. Distribute two sets of related data and questions to each student. Basketball Data, Attachment A may be used. 2. Have groups of students complete graphs and draw inferences about the data by answering questions about the similarities and differences of the graphs. Use the questions on Basketball Data, Attachment A, to prompt the discussion among the groups of students to help form their conclusions. 3. Each group should compile a report of their conclusions for one of the scenarios (e.g., great player, good player, average player, below-average player) or the teacher may assign students/groups to address each different point of view. 4. Each group reports to the rest of the class. 5. The class reaches consensus on the report contents. Instructional Tip: The four quartiles of the box plot could represent each category of players great player, good player, average player, below-average player.

3 Differentiated Instructional Support: Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s) Organize student groups to allow all students to contribute according to their strengths; e.g., calculator work, drawing conclusions, writing reports. For students who may have difficulty visualizing the relationships when using technology to graph the data, physically creating the graphs, allows them to focus on the relationship of the data. For the student who has a good grasp of this activity, pose the following situation: You are starting an expansion team and want to attract good players. What would the graph and set of data look like for the salaries of your team? The median and minimum must be the same as the other two teams and the maximum must be between the maximums of the other two teams. Extension: Ask students to find data on a topic of interest to them and to create similar questions and/or reports; Have students find statistical graphs in newspapers or magazines, and report how the graphs are informative or misleading. Vocabulary: box-and-whisker plot histogram mean median quartile range Technology Connections: graphing calculator graphing software Attachments: Attachment A, The Basketball Data Attachment B, Which Basketball Team Shall I Sign With?? Attachment C, Analytic Rubric

4 Materials and Resources: For the teacher: Two related data sets for the class work and a set for the post assessment Basketball Data (Attachment A, included as a sample) Which Basketball Team Shall I Sign With? (Attachment B, included for the post-assessment) Classroom demonstrates capability for using a graphing calculator or computer. For the student: Graphing calculator or computer with graphing software, paper and pencil. References: The basketball player salary data, Basketball Data, Attachment A and Which Basketball Team Shall I Sign With?, Attachment B, were obtained from:

5 Attachment A Basketball Data The lists below give the salaries for the Houston Rockets and the Cleveland Cavaliers. Houston Rockets Cleveland Cavaliers Player Salary($) Player Salary ($) Steve Francis 10,067,750 Zydrunas Ilgauskas 13,500,000 Maurice Taylor 7,800,000 Ricky Davis 5,000,000 Kelvin Cato 7,344,000 Michael Stewart 4,480,000 Cuttino Mobley 5,394,000 Darius Miles 4,131,000 Yao Ming 4,147,560 LeBron James 4,018,920 Moochie Norris 3,600,000 Chris Mihm 2,809,500 John Amaechi 2,610,000 Dajuan Wagner 2,471,280 Eric Piatkowski 2,460,000 Ira Newbie 2,458,500 Jim Jackson 2,225,000 Kevin Ollie 2,458,500 Bostjan Nachbar 1,396,450 Desagana Diop 2,188,840 Scott Padgett 688,679 Jelani McCoy 751,179 Adrian Griffin 688,679 Bruno Sundov 751,179 Ben Davis 688,679 Carlos Boozer 563,679 Mike Wilks 563,679 JR Bremer 563,679 Torraye Braggs 366,961 Jason Kapono 366, Looking at each set of data and without computing, estimate the mean of the annual salary of each team. If one of your estimates is larger than the other, explain why you believe that is the case. 2. Find the mean of each set of data. Did these means support your predictions? If not, why do you think this happened?

6 Attachment A (continued) Basketball Data 3. Use your calculator to construct histograms of the data. Choose the window and x-scale, so that the graphs are comparable to each other. Sketch the histograms below. 4. How do the histograms help you to understand the relative size of the means? 5. Use your calculator to make box-and-whisker plots of the two data sets on the same screen. Sketch the plots below, indicating the values for the extremes, first and third quartile scores, and the median. 6. Use the plots above to explain the strategy that management uses to hire and pay its players. Which team would be more likely to pay you better if you were a great, good, average, or below-average player? 7. Summarize how comparing the histograms and box-and-whisker plots of the two data sets gives you a "feel" for how salaries for the team are distributed.

7 Attachment B Which Basketball Team Shall I Sign With? Imagine that you are a basketball player who has the opportunity to sign with either the Golden State Warriors or the Chicago Bulls. The salaries for the teams are listed below. Chicago Bulls Golden State Warriors Player Salary($) Player Salary ($) Jalen Rose 14,279,500 Nick Van Exel 10,912,500 Eddie Robinson 6,246,950 Erick Dampier 7,842,000 Scottie Pippen 4,917,000 Avery Johnson 5,446,000 Donvell Marshall 4,545,000 Clifford Robinson 4,740,000 Tyson Chandler 3,804,360 Adonal Foyle 4,400,000 Marcus Fizer 3,727,000 Mike Dunleavy 3,332,500 Jay Williams 3,710,000 Speedy Claxton 3,000,000 Eddy Curry 3,080,000 Evan Eschmeyer 2,800,000 Jamal Crawford 2,578,000 Jason Richardson 2,696,000 Kirk Hinrich 2,098,600 Mickael Pietrus 1,661,280 Corie Blount 1,600,000 Troy Murphy 1,507,000 Gill Kendall 1,070,000 Calbert Cheaney 1,070,000 Roger Mason 563,679 Popeye Jones 1,070,000 Lonny Baxter 563,679 Brian Cardinal 663,679 Linton Johnson 366,931 Pepe Sanchez 663,679 Discuss your salary prospects with each team, assuming that you are a great, good, average, and below average player. Use histograms and box-and-whisker plots to explain your positions.

8 Attachment C Analytic Rubric Graphs Conclusions Clarity Excellent Good Fair Poor Accurate, neat, Accurate, most Accurate with Inaccurate labels, parts identified few parts extremes, identified quartiles and mean clearly designated Draws correct conclusions for each situation/ Refers to histogram to provide support for conclusions Presents conclusions in a logical sequence/ Easy to read and follow Draws correct conclusions/ Provides reasons for conclusions but does not correctly refer to histogram Presents conclusion in a logical sequence/ Difficult to follow Draws correct conclusions/ Does not provide support for conclusions No logical sequence of conclusions Does not draw correct conclusions No conclusions drawn