Stem-and-Leaf Plots, Boxplots, and Percentiles – An Example ...

determinedenchiladaUrban and Civil

Nov 25, 2013 (4 years and 1 month ago)

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Stem
-
and
-
Leaf Plots, Boxplots, and Percentiles


An Example

Corrosion of reinforcing steel is a serious problem in concrete structures located in environments
affected by severe weather conditions. For this reason, researchers have been investigating the
use of reinforcing bars made of composite material. One stu
dy was carried out to develop
guidelines for bonding glass
-
fiber
-
reinforced plastic rebars to concrete (“Design
recommendations for bond of GFRP rebars to concrete”, Journal of Structural Engineering, 196:
247
-
254). Consider the following 48 observations

of measured bond strength

for specimens
subjected to monotonic static loading

(units are giga
-
Pascals = 10
6

Nt/m
2
):


11.5

12.1


9.9


9.3


7.8


6.2


6.6


7.0

13.4

17.1


9.3


5.6


5.7


5.4


5.2


5.1


4.9

10.7

15.2


8.5


4.2


4.0


3.9


3.8


3.6


3.4

20.6

25.5

13.8

12.6

13.1


8.9


8.2

10.7

14.2


7.6


5.2


5.5


5.1


5.0


5.2


4.8


4.1


3.8


3.7


3.6


3.6


3.6


A stem
-
and
-
leaf plot of the data set is shown below.

Below the stem
-
and
-
leaf plot

the
descriptive statistics are list
ed, followed by a boxplot of the data.

Bond Strengths for GFRP Specimens




3|466667889



4|01289



5|0112224567




6|26



7|068



8|259



9|339


10|77


11|5


12|16


13|148


14|2


15|2


16|


17|1


18|


19|


20|6


21|


22|


23|


24|


25|5



̅








s = 4.8
7

GPa,
minX = 3.4 GPa, Q
1

=
4
.5 GPa,

̃






, Q
3

= 10.7 GPa,

maxX = 25.5 GPa.


Bond Strengths for GFRP Specimens



_
________________




----
|
____|____________|
-----------------------


*



*

______________________________________________________________________________

| | | | | |

| |

0

4


8 12 16 20 24 28

Bond Strength (GPa)


We see that there are two outliers, at 20.6 GPa and at 25.5 GPa. The researcher would need
to
look at these specimens to see whether there were something unusual about them. It is likely,
however, that they simply represent the extreme right
-
hand tail of the distribution of bond
strengths.


We want to compute the 40
th

percentile of the data set
. After the data have been sorted (as in the
stem
-
and
-
leaf plot), we compute (n)(p) = (48)(0.40) = 19.2. This number is not an integer, so we
round up; the 40
th

percentile will be the 20
th

observation in the sorted data set
. Looking back at
the stem
-
and
-
leaf plot, we find that the 40
th

percentile is

5.2 GPa. Forty percent of the specimens
have bond strengths no greater than 5.2 GPa.