Transcript No Slide Title

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
Disadvantage of
boxplots
• does not retain the
individual observations
• should not be used with
small data sets (n < 10)
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
Modified boxplots
• display outliers
• fencesALWAYS
mark offuse
mild
&
modified
extreme
outliers
boxplots in this class!!!
• whiskers extend to largest
(smallest) data value inside the
fence
Inner fence
Interquartile Range
Q1 –– 1.5IQR
Q3 + 1.5IQR
(IQR)
is the range
(length) of
theobservation
box
Any
outside this
Q3 -fence
Q1 is an outlier! Put a dot
for the outliers.
Q1
Q3
Modified Boxplot . . .
Draw the “whisker” from the quartiles
to the observation that is within the
fence!
Q1
Q3
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
4.5
1.3
3.5
5.0
7.2
5.9
6.4
4.5
5.5
5.6
5.3
4.1
8.0
6.3
4.4
4.8
7.2
Create a modified boxplot. Describe the distribution.
Use the calculator to create a modified boxplot.
6.9
3.2
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)
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.
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 210. The no cancer
group has outliers at 55 and 85.