1. Box-and- Whisker Plots

2. Warm-Up On Monday night, the Bulls defeated the Pacers 92-72. Here is the stat sheet: What is the mode and median of minutes played? What is the mean of points scored? 10/16/2015 2 NameMinsPts Deng2913 Boozer1913 Radmonovic10 Noah3912 Hinrich4020 Teague156 NameMinsPts Butler10 Belinelli224 Gibson2610 Hamilton339 Robinson143 Mohammed12

3. Homework Check! Any Questions? 10/16/2015 3

4. 4 Lesson Objectives: Display and interpret data on a box-and-whisker plot.

5. 10/16/2015 5 Data can be displayed in many ways. One method of displaying a set of data is with a box- and-whisker plot. Box-and-whisker plots are helpful in interpreting the distribution of data.

6. 10/16/2015 6 Let’s Review a Bit… We know that the median of a set of data separates the data into two equal parts. Data can be further separated into quartiles. first quartileThe first quartile is the median of the lower part of the data.

7. 10/16/2015 7 second quartileThe second quartile is another name for the median of the entire set of data. The third quartile is the median of the upper part of the data. Quartiles separate the original set of data into four equal parts. Each of these parts contains one-fourth of the data. Let’s Review a Bit…

8. 10/16/2015 8 Constructing a Box-and- Whisker Plot Write the data in numerical order and find the first quartile, the median, the third quartile, the smallest value and the largest value. median = 80 first quartile = 70 third quartile = 90 smallest value = 65 largest value = 100

9. 10/16/2015 9 Place a circle beneath each of these values on a number line. Constructing a Box-and- Whisker Plot

10. 10/16/2015 10 Draw a box with ends through the points for the first and third quartiles. Then draw a vertical line through the box at the median point. Now, draw the whiskers (or lines) from each end of the box to the smallest and largest values. Constructing a Box-and- Whisker Plot

11. 10/16/2015 11 Special Case: You may see a box-and-whisker plot, like the one below, which contains an asterisk. Sometimes there is ONE piece of data that falls well outside the range of the other values. This single piece of data is called an outlier. If the outlier is included in the whisker, readers may think that there are grades dispersed throughout the whole range from the first quartile to the outlier.

12. 10/16/2015 12 Note: Box-and-whisker plots are sometimes called box plots. When analyzing a set of data, it is often helpful to draw a graphical representation of the data. One such graph which shows the quartiles and extreme values of the data is called a box-and-whisker plot.

13. 10/16/2015 13 Meet Mr. Whiskerswagg Mr. Whiskerswagg has 13 students in his Modern Algebra class at the University of MathSwagg. These students just took a test. Suppose Mr. Whiskerswagg wants to display this data in a box-and-whisker plot. First, he must arrange the data in numerical order.

14. 10/16/2015 14 Here’s the Data Set First order the numbers Find the median, lower quartile, upper quartile, and least value (LV) and greatest value (GV). 8085907260 4281745061 488881 42, 48, 50, 60, 61, 72, 74, 80, 81, 81, 85, 88, 90

15. 10/16/2015 15 Construct the Box-and- Whisker Plot First, draw a number line. Assign a scale to the number line that includes the extreme values. Plot dots to represent the extreme values (LV) and (GV), the upper and lower quartiles (LQ) and (UQ), and the median (M). 40506070 80 90 100 LQLQ LVLV M UQUQ GVGV

16. 10/16/2015 16 Construct the Box-and- Whisker Plot Next, draw a box around the interquartile range. Mark the median by a vertical line through its point in the box. The median line will not always divide the box into equal parts. Draw a segment from the lower quartile to the greatest value. These segments are the whiskers of the plot. 40506070 80 90 100

17. 10/16/2015 17 About the Whiskers… Even though the whiskers are different lengths, each whisker contains at least one fourth of the data while the box contains at least one half of the data.

18. 10/16/2015 18 Example 2 Twelve members of the Oswego High School Boosters are selling programs for the baseball game. The number of programs sold by each person is listed below: Member# Sold Member# Sold George51Kendra55 Vinette69Carmen39 Tomas46Danny71 Anthony27Eddie54 Marlene60Jason46 Kohana53Nashoba23

19. 10/16/2015 19 Make a box-and-whisker plot of this data. First arrange the data in numerical order. Find the extreme values (LV) and (GV) Find the median (M) Find the LQ and UQ Member# SoldMember# Sold George51Kendra55 Vinette69Carmen39 Tomas46Danny71 Anthony27Eddie54 Marlene60Jason46 Kohana53Nashoba23 Example 2

20. 10/16/2015 20 Now Let’s Draw It 30 20 40 50 60 70 80 Median (M) = 52 Extreme Values LV = 23 and GV = 71 Lower Quartile (LQ) = 42.5 Upper Quartile (UQ) = 57.5

21. Exit Slip Today I learned about ____________. –The easiest thing to do was ________. –The hardest thing to do was ________. This week, we’ve learned about _____. –I’m really good at ______________. –I need help with _______________. 10/16/2015 21

22. Assignment pg.378 #9, 11, 12, 15-17 10/16/2015 22