Algebra 1 Unit 10: Culminating Task Name ______________________________ Period________ Date____________ How High Can You Jump? Statistical Question: “How high can you jump?” “Is this different for males and females?” Step 1: Collect perceptual data. We will take a class poll and fill in the accompanying two-way frequency table. Question: “Do you think you have a “good” vertical jump?” Male Female Total Yes No Total a) Find the joint and marginal relative frequencies and put them next to each number in the table. b) Find the conditional relative frequencies and list them below. Percent of males who think they have a good vertical jump: Yes________, No___________ Percent of females who think they have a good vertical jump: Yes________, No___________ Step 2: Collecting actual data. Work with your group and we will then collect all group results. Determine the height and vertical jump of all the members of your group. Each member gets three attempts, take their best overall height. Use the table below to collect your data. Name (Standing) Height Standing Reach Height (inches) Jumping Reach Height (inches) *Vertical Jump *Vertical Jump = Jumping Reach Height – Standing Reach Height 1 Now use the whole class data to determine the mean and five number-summary. Fill in the table below. Mean Minimum 1st Quartile Median 3rd Quartile Maximum Whole Class Males Females Step 3: Organize your data into a side-by-side box plot to compare the vertical jump of males and females in our class. What conclusion can be drawn from your side-by-side box plots? (Look back at the statistical question) Make sure to cite actual data from above in writing your conclusion. 2 Step 4: How good is “good”? Go online and find the vertical jump of top male and female athletes. Choose 10-15 of each gender and calculate the mean and five number-summary for males and females. You can choose any athletes you want…below are some websites to get you started. Females: http://overseasbasketballcombines.com/2013-new-orleans/ Males: http://www.topendsports.com/testing/records/vertical-jump.htm Top Athletes Males Mean Minimum 1st Quartile Median 3rd Quartile Maximum Females Step 5: Make two comparative box-plots to show the vertical jump of our class’ vertical jumps compared to professional athletes. What can you summarize regarding the comparative box plots above? Be sure to cite actual data in your conclusion. 3 Step 6: Bivariate Data. Statistical Question: “Does your height effect how high you can jump?” Construct a scatterplot below for all of the students in our class. Label each axis with an appropriate variable name. a) What type of relationship between height and vertical jump, if any, is shown in the scatterplot above? b) Use your graphing calculator to determine the equation of the line of best fit [diagnostics on]. c) What is the slope of the line and what does the slope mean in terms of this bivariate data? d) What is the correlation coefficient? What does this tell you about the equation you found? 4 e) Do you think that this correlation would also be true for the professional athletes that you researched? Explain your answer. Step 7: Summary a) After completing this study, were you surprised by the results? b) Name three things you learned as a result of completing this study. Be specific and cite specific examples or data from above. c) What are the limitations to this study? That is, what are some things that could be improved upon in this study? Use a separate sheet if necessary. 5