Bowling for Box Plots © Copyright 2015 – all rights reserved

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

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

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

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

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

Continued Did you get? Frame # © Copyright 2015 – all rights reserved

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? © Copyright 2015 – all rights reserved

Box Plot Friday League Saturday League © Copyright 2015 – all rights reserved

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

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

Bowling Results – students may work in their groups for 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

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