1. Boxplots

2. Why use boxplots? ease of construction convenient handling of outliers
construction is not subjective (like histograms)
Used with medium or large size data sets (n > 10)
useful for comparative displays

3. Disadvantage of boxplots
does not retain the individual observations
should not be used with small data sets (n < 10)

4. How to construct find five-number summary Min Q1 Med Q3 Max
draw box from Q1 to Q3
draw median as center line in the box
extend whiskers to min & max

5. ALWAYS use modified boxplots in this class!!!
display outliers
fences mark off mild & extreme outliers
whiskers extend to largest (smallest) data value inside the fence
ALWAYS use modified boxplots in this class!!!

6. Interquartile Range (IQR) – is the range (length) of the box
Inner fence
Interquartile Range (IQR) – is the range (length) of the box
Q3 - Q1
Q1 – 1.5IQR
Q IQR
Any observation outside this fence is an outlier! Put a dot for the outliers.

7. Modified Boxplot . . .
Draw the “whisker” from the quartiles to the observation that is within the fence!

8. Any observation outside this fence is an extreme outlier!
Outer fence
Q1 – 3IQR
Q3 + 3IQR
Any observation between the fences is considered a mild outlier.
Any observation outside this fence is an extreme outlier!

9. For the AP Exam . . .
. . . you just need to find outliers, you DO NOT need to identify them as mild or extreme.
Therefore, you just need to use the
1.5IQRs

10. A report from the U.S. Department of Justice gave the following percent increase in federal prison populations in 20 northeastern & mid-western states in 1999.
Create a modified boxplot. Describe the distribution.
Use the calculator to create a modified boxplot.

11. Symmetrical boxplots
Approximately symmetrical boxplot
Skewed boxplot

12. Evidence suggests that a high indoor radon concentration might be linked to the development of childhood cancers. The data that follows is the radon concentration in two different samples of houses. The first sample consisted of houses in which a child was diagnosed with cancer. Houses in the second sample had no recorded cases of childhood cancer.

13. Cancer
No Cancer
Create parallel boxplots. Compare the distributions.

14. Cancer’s 5 # Summary:
No Cancer’s 5 # Summary:
Min Q1 Med Q3 Max
IQR = 11
Min Q1 Med Q3 Max
IQR = 18

15. Calculating the fence (Cancer):
Q1 – 1.5 IQR
11 – 1.5*11 =
Q IQR
*11 = 38.5
Calculating the fence (No Cancer):
Q1 – 1.5 IQR
8.5 – 1.5*18 =
Q IQR
*18 = 53.5

16. Creating a Box Plot
Cancer
No Cancer
Radon

17. Cancer
No Cancer
100
200
Radon
The median radon concentration for the no cancer group is lower than the median for the cancer group. The range of the cancer group is larger than the range for the no cancer group. Both distributions are skewed right. The cancer group has outliers at 39, 45, 57, and The no cancer group has outliers at 55 and 85.