THE FIVE NUMBER SUMMARY
You give me 10 minutes, I’ll
give you…
 A basic understanding of the “5-number
summary”
 A way to depict this summary visually
 The definition of an outlier
Elements of the FNS
 Minimum
 Lower Quartile
 Median
 Upper Quartile
 Maximum
Calculating the Median
 When n is odd…

Median = [(n+1)/2]th observation
 When n is even…

Median =
AVG ([n/2]th observation; [(n/2) + 1]th observation)
Calculating the Quartiles
 The lower quartile is the median of the
lower 50% of data.
 The upper quartile is the median of the
upper 50% of data.
 DO NOT include the median of the entire
sample when calculating the quartiles.
Examples
 3
5
 12
14
8
18
12
34
14
61
15
173
20
Boxplot
 The five-number summary forms the
basis for a graph called a boxplot.
Boxplots are especially useful for
comparing distributions of a quantitative
variable across two or more groups.
 Examples include annual rainfall in
various U.S. cities and the runs scored
per game for teams in the National
League and in the American League.
Parts of Boxplot
 Box
 Whiskers
Outliers
 An outlier is any
observation falling
more than 1.5 times
the interquartile range
away from the nearer
quartile.
 IQR = Qu - Ql
Examples
3
5
8
12
14
15
•IQR = 10
•Outlier is greater than 15 + 1.5(10) = 30
•Outlier is less than 5 - 1.5(10) = -10
•No outliers in this sample
12
14
18
34
61
173
•IQR = 47
•Outlier is greater than 61 + 1.5(47) = 131.5
•Outlier is less than 14 - 1.5(47) = -56.5
•173 is an outlier in this example
20
Modified boxplots
 Modified boxplot’s whiskers
only extend to the most
extreme non-outlier values
 All outliers are represented
by a symbol (*) on the
modified boxplot
With your partner…
MLB Activity
Do it.
Credits
Sports photos courtesy of www.ESPN.com
Graphs courtesy of www.vertex42.com and
www.support.sas.com
Video courtesy of Discovery Channel
Song courtesy of Jackson 5, ABC, Motown Records, 1970
Celebrity photo courtesy of www.IMDB.com