1. Statistics
Boxplots

2. Exploring Data
We are using the descriptive statistics to summarize our sample (and, hopefully, our population) in just a few numbers

3. Exploring Data
The “five-number summary” is: the min Q1 the median Q3 the max

4. Boxplots
There is a graph statisticians use to show this summary: the box plot (or boxplot)

5. Boxplots
The boxplot (a.k.a. box and whisker diagram) is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum

6. Boxplots

7. BOXPLOTS
IN-CLASS PROBLEM
Daily high temperatures Feb 2008 for Fairbanks, Alaska: 14, 12, 17, 25, 10, -1, -8, -15, -7, 0, 5, 14, 18, 14, 16, 8, -15, -13, -17, -12, 0, 1, 9, 12, 14, 7, 6, 8 Create a Boxplot

8. What do we need for a Boxplot?
BOXPLOTS
IN-CLASS PROBLEM
What do we need for a Boxplot?

9. BOXPLOTS
IN-CLASS PROBLEM
Daily high temperatures Feb 2008 for Fairbanks, Alaska: 14, 12, 17, 25, 10, -1, -8, -15, -7, 0, 5, 14, 18, 14, 16, 8, -15, -13, -17, -12, 0, 1, 9, 12, 14, 7, 6, 8 Find the 5-number summary

10. BOXPLOTS
IN-CLASS PROBLEM
Min = Q1 = Median = Q3 = Max =

11. BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Notice they’re all in order at the bottom of your list! YAY!

12. Min = -17 Now for the box! Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Now for the box! Q1 = -4 Median = 7.5 Q3 = 14 Max = 25

13. Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Min!
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
Min!

14. Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Q1!
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
Q1!

15. Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Median!
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
Median!

16. Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Q3!
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
Q3!

17. Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Max!
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
Max!

18. Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Box!
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
Box!

19. Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25 Whiskers!
BOXPLOTS
IN-CLASS PROBLEM
Min = -17 Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
Whiskers!

20. Questions?

21. Outliers
Because the min and max may be outliers, a variation on the boxplot includes “fences” to show where most of the data occurs

22. Outliers
Lower fence: Q * IQR Upper fence: Q * IQR

23. Min = -17 What is the IQR? Q1 = -4 Median = 7.5 Q3 = 14 Max = 25
OUTLIERS
IN-CLASS PROBLEM
Min = -17 What is the IQR? Q1 = -4 Median = 7.5 Q3 = 14 Max = 25

24. OUTLIERS
IN-CLASS PROBLEM
Min = -17 IQR=14-(-4)=18 Q1 = -4 What is the Median = 7.5 lower fence? Q3 = 14 Max = 25

25. OUTLIERS
IN-CLASS PROBLEM
Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence = Median = 7.5 Q1-1.5*IQR Q3 = (18) Max = 25 = -31

26. OUTLIERS
IN-CLASS PROBLEM
Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 What is the Q3 = 14 upper fence? Max = 25

27. OUTLIERS
IN-CLASS PROBLEM
Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 Upper fence= Q3 = 14 Q3+1.5*IQR Max = (18)=41

28. OUTLIERS
IN-CLASS PROBLEM
Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 Upper fence=41 Q3 = 14 So, do we have Max = 25 any outliers?

29. OUTLIERS
IN-CLASS PROBLEM
Min = -17 IQR=14-(-4)=18 Q1 = -4 Lower fence=-31 Median = 7.5 Upper fence=41 Q3 = 14 Max and Min are Max = 25 inside the fence!

30. Outliers
How outliers are shown in a boxplot

31. Types of Boxplots

32. Questions?

33. Boxplots
Boxplots are typically used to compare different groups

34. Data Summary Table from a Ball-bouncing Experiment
Boxplots
Data Summary Table from a Ball-bouncing Experiment
Super
Ball
Wiffle
Golf
Splash
SpongyBall
Minimum 66 38 70 7 44 Q1 71 45 75 14 58
Median 76 48 78
16.5 60 Q3 50 80 23 62
Maximum 91 90 28 67

35. Boxplots

36. Boxplots

37. BOXPLOTS
IN-CLASS PROBLEM
What differences?

38. Boxplots
Unfortunately it is almost impossible to get a true boxplot using Excel

39. Boxplots
Unfortunately it is almost impossible to get a true boxplot using Excel (there are several YouTube videos showing how to get one…

40. Boxplots
Unfortunately it is almost impossible to get a true boxplot using Excel (there are several YouTube videos showing how to get one… but they are all wrong…)

41. Questions?