04-07 boxplotsimulation

8/2/2019 04-07 BoxPlotSimulation

1/3

Normal Boxplots

48.58 66.16 69.71 68.45 39.57

32.77 58.67 58.04 50.62 52.99

34.12 56.49 33.15 2.37 61.95

28.97 50.69 71.80 47.83 19.82

62.48 45.41 57.46 46.26 45.67

74.34 58.27 45.50 51.49 44.26

47.07 26.03 71.69 40.48 61.76

55.28 60.14 31.28 52.90 82.5656.33 7.02 47.70 60.01 56.42

38.18 57.30 44.00 27.64 15.29

Min Q1 Q2 Q3 Max

Item X Y Sample 2.37 39.80 50.66 58.57 82.56 Item X Y

Min 2 1.5 Expected 15.10 39.88 50.00 60.13 84.90 Min 15 4.5

Q1 40 1.5 Q1 40 4.5

Q1 40 2.5 Q1 40 5.5

Q3 59 2.5 Q3 60 5.5Q3 59 0.5 Q3 60 3.5

Q1 40 0.5 Q1 40 3.5

Q1 40 2.5 Q1 40 5.5

Q3 59 1.5 Q3 60 4.5

Max 83 1.5 Max 85 4.5

3

Q2 51 0.5 Q2 50 3.5

Q2 51 2.5 Q2 50 5.5

Q3 59 2.5 Q3 60 5.5

Q3 59 0.5 Q3 60 3.5

Expected Box Plot Setup

Sample of 50 Items

Sample Box Plot Setup

Mean 50

St. Dev. 15

0 20 40 60 80 100

Sample

Normal

Source See Rick Hesse, "Box and Whiskers Plots," Decision Line, March, 1997,

pp. 17-18. You can change the display format of sample or quartiles to see more

decimals. Expected statistics are based on the normal distribution. The min and

max are F-1[(i-0.5)/n] using i = 1, i = 50, and n = 50. For further explanation, see

Ralph B. D'Agostino and Michael A. Stephens, Goodness of Fit Techniques

(Marcel Dekker, Inc., 1986, p. 25.

Press F9 for anew sample.

Note You can

change the meanand st. dev.

Exercises (1) Examine the normal boxplot (shown in blue). In a normal

distrbution, the quartiles are 0.675 standard deviations from the mean, so

the box is narrower than the range. Is this true in most of the samples, as you

press F9 a few times? (2) As you press F9 a few times, compare the samplequartiles (shown in red) to the normal boxplot (shown in blue). How stable

are the quartiles from sample to sample? (3) Watch the end points of the

sample boxplot as you press F9 a few times. Are the end points more or lessstable than the quartiles? (4) In general, did your samples usually resemble

the expected normal boxplot? (4) press F9 ten times. What percentage of thetime did you get a boxplot that definitely did notlook like the normalboxplot? What is the implication?

Learning Stats

Copyright 2007

by

Th e McGraw-Hill Companies

This spreadsheet is intended solely

for educational purposes by licensed

users ofLearningStats . It may not

be copied or resold for pro fit.


2/3

Uniform Boxplots

28.60 63.72 83.72 35.68 31.90

40.92 40.06 72.56 22.64 37.28

72.20 36.49 84.69 46.42 67.94

29.70 66.20 81.60 71.07 71.86

42.79 36.07 40.75 64.35 40.96

27.82 79.25 41.96 58.85 27.56

67.89 69.32 40.31 29.38 65.45

54.70 22.74 69.11 38.55 65.8153.99 72.78 79.10 47.68 76.22

56.85 71.17 66.26 22.22 83.31

Min Q1 Q2 Q3 Max


Min 22 1.5 Expected 16.00 33.25 50.50 67.75 85.00 Min 16 4.5

Q1 38 1.5 Q1 33 4.5

Q1 38 2.5 Q1 33 5.5

Q3 71 2.5 Q3 68 5.5Q3 71 0.5 Q3 68 3.5

Q1 38 0.5 Q1 33 3.5

Q1 38 2.5 Q1 33 5.5

Q3 71 1.5 Q3 68 4.5

Max 85 1.5 Max 85 4.5

3

Q2 56 0.5 Q2 51 3.5

Q2 56 2.5 Q2 51 5.5

Q3 71 2.5 Q3 68 5.5

Q3 71 0.5 Q3 68 3.5


Sample of 50 Items


Min 16

Max 85

0 20 40 60 80 100

Sample

Uniform

Source See Rick Hesse, "Box and Whiskers Plots," Decision Line , March,

1997, pp. 17-18. You can change the display format of sample or quartiles to

see more decimals. Expected statistics are based on the uniform distribution.


Note You can

change the minand max.

Exercises (1) Examine the uniform boxplot (shown in blue). How is the

position of the quartiles and end points determined? (2) As you press F9

a few times, compare the sample quartiles (shown in red) to the uniform

boxplot (shown in blue). How stable are the quartiles from sample to

sample? (3) Watch the end points of the sample boxplot as you press F9

a few times. Are the end points more or less stable than the quartiles?

(4) In general, did your samples usually resemble the expected uniform

boxplot? (5) press F9 ten times. What percentage of the time did you

get a boxplot that definitely did notlook like the uniform boxplot?What is the implication?

Learning Stats

Copyright 2007

by

The McGraw-Hill Companies

Th is spreadsheet is intended solely

for educational purposes by licensedusers ofLearningStats . It may not

be copied or resold for pro fit.


3/3

Skewed Boxplots2

1.35 1.24 8.30 0.46 1.38 Slight

1.11 0.93 0.18 0.11 0.39 Medium

0.74 0.22 0.34 0.33 0.30 Strong

7.00 11.85 0.73 3.47 1.22 D.F. 2

1.70 2.12 2.53 0.45 1.33 Control 3

0.48 1.44 0.39 2.60 0.65

1.43 0.03 2.39 0.06 0.16

1.21 0.36 0.52 0.28 0.360.60 1.01 7.72 4.79 4.420.70 0.46 0.23 0.21 4.18

Min Q1 Q2 Q3 Max


Min 0.03 1.5 Expected 0.02 0.58 1.39 2.77 9.21 Min 0.02 4.5

Q1 0.36 1.5 Q1 0.58 4.5

Q1 0.36 2.5 Q1 0.58 5.5

Q3 1.63 2.5 Q3 2.77 5.5Q3 1.63 0.5 Q3 2.77 3.5

Q1 0.36 0.5 Q1 0.58 3.5

Q1 0.36 2.5 Q1 0.58 5.5

Q3 1.63 1.5 Q3 2.77 4.5

Max 11.85 1.5 Max 9.21 4.5

3

Q2 0.74 0.5 Q2 1.39 3.5

Q2 0.74 2.5 Q2 1.39 5.5

Q3 1.63 2.5 Q3 2.77 5.5

Q3 1.63 0.5 Q3 2.77 3.5

Degree of Skewness


Sample of 50 Items


0 5 10 15 20

Sample

Expected

Source See Rick Hesse, "Box and Whiskers Plots,"Decision Line, March,

1997, pp. 17-18. You can change the display format of sample or quartiles to

see more decimals. Expected statistics are based on the chi-square

distribution. The min and max are F-1[(i-0.5)/n] using i = 1, i = 50, and n =

50. For further explanation, see Ralph B. D'Agostino and Michael A.

Stephens, Goodness of Fit Techniques (Marcel Dekker, Inc., 1986, p. 25.


Note You can

change theskewness.

Exercises (1) Examine the expected boxplot (shown in blue). Examine the

position of the median within the box, and the length of the each tail. Does itsappearance reflect the desired degree of skewness (slight, medium, strong)?(2) As you press F9 a few times, compare the sample quartiles (shown in red)

to the expected boxplot (shown in blue). How stable are the quartiles from

sample to sample? (3) Watch the end points of the sample boxplot as youpress F9 a few times. Are the end points more or less stable than the

quartiles? (4) In general, did your samples usually resemble the expected

boxplot? (5) press F9 ten times. What percentage of the time did you get aboxplot that definitely did notlook like the expected boxplot? What is the

implication?

Learning Stats

Copyright 2007

by

Th e McGraw-Hill Companies

Th is spreadsheet is int ended solely

for educational purposes by licensed

users ofLearningStats . It may not

be copied or resold for pr ofit.

04-07 boxplotsimulation

Documents