1. Bowling for Box Plots © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

2. A Box Plot is…… A box and whisker plot is a horizontal or vertical graphical representation of the distribution of data. – The end points are the minimum and maximum values (or whiskers) connected to a rectangular box – The box’s ends represent the first and third quartiles (Q1 & Q3) with an embedded line parallel to the ends representing the median of the data. © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

3. Review of Box Plots Step 1- List numbers from least to greatest. Step 2- Find the five number summary. – Minimum: Least value – Maximum: Greatest Value – Median: The middle value or average of the two middle values. – Q1: The median of the lower half of the data. – Q3: The median of the upper half of the data. Step 3- Create a number line with appropriate values. Step 4- Plot a point for the five values from the five number summary. Step 5- Draw a box from Q1 to Q3, a vertical line through the median, and horizontal “whiskers” that extend from Q1 to the minimum and Q3 to the maximum. For Further Analysis: Step 6- Calculate the IQR (Q3-Q1) Step 7- Multiply IQR by 1.5 to determine if there are any outliers. © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

4. Bowling In the game of bowling, a player takes a bowling ball and attempts to knock down 10 pins on a total of up to two turns. Each frame includes two chances or rolls to knock down 10 pins. Your frame total is the total number of pins for that frame. A strike (X) is marked when you knock down all the pins with your first roll. You score 10 pins plus your next two rolls in total pins. A spare (/) is marked when you knock down all the pins with two rolls. Your score for that frame would be 10 plus your next roll. © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

5. Other information You can bowl between 0-300 (perfect game) Increase your score by increasing your “marks”: – Strikes help the most. – Spares help the second most. © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

6. Try this… What is the total score? You have 1 minute! Frame:123 Result:X7/7 2 Frame Score: Running Total: © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

7. Continued Did you get? Frame # 1-- 20 2--37 3--46 © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

8. Guided Practice A bowling league on Friday night scored the following scores: 225, 214, 247, 196, 276, 202, 227, 182, 226, 176, and 223. The Saturday morning league scored these scores: 212, 192, 199, 215, 175, 247, 258, 216, 215, 242, 236, and 158. Task: Compare the league scores by creating two box plots and analyzing the data. What conclusions can you make? 225225 214214 247247 196196 276276 202202 227227 182182 226226 176176 223223 © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

9. Box Plot Friday League Saturday League © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

10. Results What is the median of the Friday and Saturday leagues? – Which is greater? – What caused the shift in medians? What is the IQR (Q3-Q1)? – Which shows a larger “spread” of the data via the IQR? – What does this tell you about the middle 50% of the data of both box plots? – Calculate IQR * 1.5. Any value + or – (IQR* 1.5) is an outlier. Are there any outliers? – What effects do(es) the outlier(s) have on the mean, median, and range? © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

11. Independent Practice— Est. 30 minutes You will assemble into groups of 3 to 4 and bowl one game per person. Break up roles to use time efficiently: one bowler, one scorer, one setup person, and one cleanup person. Once you have finished, gather the four scores for reporting. © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

12. Bowling Results – students may work in their groups for 10-15 minutes to answer the following questions. Answers will be reviewed during class time. The teacher will tabulate the data into GeoGebra before students answer the following questions: What is the median of the F? – Which is greater? – What caused the shift in medians? What is the IQR (Q3-Q1)? – Which shows a larger “spread” of the data via the IQR? – What does this tell you about the middle 50% of the data of both box plots? – Calculate IQR * 1.5. Any value + or – (IQR* 1.5) is an outlier. Are there any outliers? – What effects do(es) the outlier(s) have on the mean, median, and range? © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org

13. Exit Slip What can you conclude about weight of cars in the US, Asia, and Europe via the median and IQR? © Copyright 2015 – all rights reserved www.cpalms.orgwww.cpalms.org