1. Chapter 5
Stories Quantitative Data Tell

2. How far out is too far? >1.5 times IQR
Outliers - Adding Fences to Box & Whisker Plots
How far out is too far? >1.5 times IQR
Consider the following data set:
1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24
Find
Q1= Q2 = 9 Q3= IQR = 6
1.5 * IQR = 9

3. Construct the Box and Whisker Plot for:
1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24
Q1= Q2 = 9 Q3= IQR = IQR = 9
That outlier sort of makes the plot look weird

4. Create Fences
Lower Fence at Q IQR
Upper Fence at Q IQR
Note: Fences are not typically drawn on the Box & Whisker Plot. Simply connect the whisker from the box to the furthest dot within the fence. The outliers are shown as dots, but not connected.

5. Q1 - 1.5IQR = 6 - 9 = -3 (not on our plot) and
Create fences at (we will use a light dotted line for 
illustration) 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24
Q IQR = = -3 (not on our plot)
and
Q IQR = = 21 (is on our plot)
Q1= Q2 = 9 Q3= IQR = IQR = 9
Draw a whisker to the furthest point that 
falls within the fence. Then use dots at outliers

6. So the final Box and Whisker plot for 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24 would look like
Q1= Q2 = 9 Q3= IQR = IQR = 9

7. Consider the following data set: 21, 23, 24, 25, 29, 33, 49 Find
Outliers - Adding Fences to Box & Whisker Plots
Consider the following data set:
21,  23,  24,  25,   29,  33,  49
Find
Q1= Q3= IQR = 10
1.5 * IQR = 15

8. Construct the Box and Whisker Plot for:
21,  23,  24,  25,   29,  33,  49
Q1= Q3= IQR = * IQR = 15
That outlier sort of makes the plot look weird

9. Q1 - 1.5IQR = 23 - 15 = 8 (not on our plot) and
Create fences at (we will use a light dotted line for illustration) 21,  23,  24,  25,   29,  33,  49
Q IQR = = 8 (not on our plot)
and
Q IQR = = 48 (is on our plot)
Draw a whisker to the furthest point that falls within the fence. In this case, the point is 33. Then use dots at outliers

10. So the final Box and Whisker Plot for
21,  23,  24,  25,   29,  33,  49
would be:

11. Note: Can you find the mistake in this video?
Comparing Histograms
Note: Can you find the mistake in this video?
Video

12. Would you want sandwich A or sandwich B? Why?
40 students were asked to taste two different chicken sandwiches. The students were asked to score the sandwiches, with 1 being awful and 6 being great. The charts show the scores for each sandwich. A B
Would you want sandwich A or sandwich B? Why?

13. Sandwich A has a symmetric graph. The mean and median are 3.5 B
Sandwich A has a symmetric graph. The mean and median are 3.5
Sandwich B requires some work
Count in 20 and 21 the median is 4
Calculate the mean:
(7*1) + (7*2)+(5*3)+(9*4)+(4*5)+(8*6) = 3.5 40

14. Now Consider the Boxplot for each Sandwich
Did you know Boxplots could be Vertical?

15. Practice Matching Histograms and Boxplots Online Activity

16. Back-to-Back Stem and Leaf Plots
Double the Fun

17. Parallel Box Plots (y-axis must be the same)
Video