Boxplots

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 gt 10)
• useful for comparative displays

3
Disadvantage of boxplots

• does not retain the individual observations
• should not be used with small data sets (n lt 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
Modified boxplots

• 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
Inner fence
Interquartile Range (IQR) is the range (length)
of the box Q3 - Q1
Q1 1.5IQR
Q3 1.5IQR
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

• 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.
• 5.9 1.3 5.0 5.9 4.5 5.6 4.1 6.3 4.8 6.9
• 4.5 3.5 7.2 6.4 5.5 5.3 8.0 4.4 7.2 3.2
• Create a modified boxplot. Describe the
  distribution.

Use the calculator to create a modified boxplot.
9
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. (see data sets on next slide)
10
Cancer 10 21  5 23 15 11 9 13 27 13 39
22 7 20 45 12 15 3 8   11 18 16 23 16
9 57 16 21 18  38  37  10 15  11  18  210  22
11 16 17 33 10 No Cancer 9 38 11 12 29
5 7 6 8 29 24 12 17 11 11 3  9 33 17
55   11 29 13 24 7 11 21 6 39 29 7 8
55  9 21 9 3 85 11 14 Create parallel
boxplots.  Compare the distributions.
11
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 210. The no
cancer group has outliers at 55 and 85.