Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Lab8: Graphical Presentation of Data Michael Akritas
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Box Plots Computer Activity: One-Sample Box-Plot Computer Activity: Comparative Box Plots
Stem-and-Leaf Diagrams Computer Activity
Histograms Computer Activities
Bar Graphs and Pie Charts Computer Activity Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity: One-Sample Box-Plot Computer Activity: Comparative Box Plots
The five number summary and outliers I
The median, minimum, maximum, 25th percentile and 75th percentile which are called the five-number summary of the data.
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An observation larger than Q3 + 1.5*IQR is called a mild outlier on the right. An observation larger than Q3 + 3*IQR is called an extreme outlier on the right. An observation smaller than Q1 - 1.5*IQR is called a mild outlier on the left. An observation smaller than Q1 -3*IQR is called an extreme outlier on the left.
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A boxplot is a graphical display of the 5 number summary. The box plot displays outliers as stars. Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity: One-Sample Box-Plot Computer Activity: Comparative Box Plots
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A study of strength properties of high-performance concrete, with super plasticizers and certain binders, obtained flexural strength measurements of 27 concrete beams.
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The measurements are given at: http: //www.stat.psu.edu/∼mga/401/Data/MPA.data.txt
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To get the five-number summary do: Stat>Basic Statistics>Display Descriptive Statistics > Double click C1, OK
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To do the box plot do: Graph>Boxplot>Select ”One Y, Simple”, OK>Enter C1, OK
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Report the five number summary, and copy and past the box plot on the word document.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity: One-Sample Box-Plot Computer Activity: Comparative Box Plots
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As the name suggests, comparative box plots are used for comparing two or more samples.
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(Exercise 6.8-4) An experiment examined the effect of temperature on the strength of new concrete. After curing for several days at 20o C, specimens were exposed to temperatures of -8o C, or 15o C for 28 days, at which time their strengths were determined.
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The measurements are given at: http://www.stat.psu.edu/∼mga/401/Data/Concr. Strength.Data.txt
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To do the box plot do: Graph>Boxplot> Select ”Multiple Y’s Simple”, OK > Enter the two data columns, OK
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Copy and past the box plot on the word document. Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Constructing a Stem-and-Leaf Display
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Constructing a Stem-and-Leaf Display The basic steps for presenting a data set x1 , . . . , xn by a stem-and-leaf diagram are:
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Constructing a Stem-and-Leaf Display The basic steps for presenting a data set x1 , . . . , xn by a stem-and-leaf diagram are: 1. Break each observation xi in two parts 1.1 The stem, which consists of the beginning digit(s) of xi , and 1.2 the leaf, which consists of the remaining digit(s) of xi .
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Constructing a Stem-and-Leaf Display The basic steps for presenting a data set x1 , . . . , xn by a stem-and-leaf diagram are: 1. Break each observation xi in two parts 1.1 The stem, which consists of the beginning digit(s) of xi , and 1.2 the leaf, which consists of the remaining digit(s) of xi .
2. Form a vertical column listing the stem values.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Constructing a Stem-and-Leaf Display The basic steps for presenting a data set x1 , . . . , xn by a stem-and-leaf diagram are: 1. Break each observation xi in two parts 1.1 The stem, which consists of the beginning digit(s) of xi , and 1.2 the leaf, which consists of the remaining digit(s) of xi .
2. Form a vertical column listing the stem values. 3. Write each leaf value in a horizontal column on the right of the corresponding stem.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Constructing a Stem-and-Leaf Display The basic steps for presenting a data set x1 , . . . , xn by a stem-and-leaf diagram are: 1. Break each observation xi in two parts 1.1 The stem, which consists of the beginning digit(s) of xi , and 1.2 the leaf, which consists of the remaining digit(s) of xi .
2. Form a vertical column listing the stem values. 3. Write each leaf value in a horizontal column on the right of the corresponding stem. 4. Display counts on the left margin.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Example (Solar Intensity in Southern Australia) A stem-and-leaf display of n = 40 solar intensity measurements (watts/m2 ) on different days follows:
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Example (Solar Intensity in Southern Australia) A stem-and-leaf display of n = 40 solar intensity measurements (watts/m2 ) on different days follows: 4 8 11 18 (4) 18 14 8 2
64 65 66 67 68 69 70 71 72
3 0 0 0 5 0 0 0 0
3 2 1 1 7 0 1 1 8
6 2 9 4 7 2 2 3
7 8 7 9 3 4 6
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4 6
5 6
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Stem: Hundreds and tens digits; Leaf: Ones digits Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Choice of Stems in a Stem-and-Leaf Diagram The number of stems used plays an important role in our ability to see interesting features of the data.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Choice of Stems in a Stem-and-Leaf Diagram The number of stems used plays an important role in our ability to see interesting features of the data. Thus, a one-digit stem (only hundreds) is too crude:
6L 6H 7
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Michael Akritas
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Lab8: Graphical Presentation of Data
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Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Choice of Stems in a Stem-and-Leaf Diagram The number of stems used plays an important role in our ability to see interesting features of the data. Thus, a one-digit stem (only hundreds) is too crude:
6L 6H 7
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On the other hand, in a display with three-digit stems (the data consists of decimal points) the information about the shape of the distribution would be compromised by the excessive detail. Michael Akritas
Lab8: Graphical Presentation of Data
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Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Choice of Stems in a Stem-and-Leaf Diagram Stems can be broken up, if needed to get a better display, using repeated or stretched stems:
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Choice of Stems in a Stem-and-Leaf Diagram Stems can be broken up, if needed to get a better display, using repeated or stretched stems:
Example (US beer production (in millions barrels) for different quarters during 1975-1982) In this figure, stem 4 has been split into 4L for the ’low’ leafs (0, 1, 2, 3, 4), while 4H hosts the ’high’ leafs. 5H 5L 4H 4L 3H
5 0 6 1 5
2 6 1 6
2 7 1 6
3 8 2 6
Michael Akritas
3 8 2 9
4 9 4 9
9 4
4
4
4
4
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
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Do a stem and leaf plot of the MPA data in C1 using the commands: Graph>Stem and leaf> Select C1, OK
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Copy and paste in the word document.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activities
The Basic Steps 1. Divide the range of the data values into consecutive intervals.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activities
The Basic Steps 1. Divide the range of the data values into consecutive intervals. 2. Define the end points of the intervals with one more decimal than used for the data set.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activities
The Basic Steps 1. Divide the range of the data values into consecutive intervals. 2. Define the end points of the intervals with one more decimal than used for the data set. 3. Count the number of data points that fall in each interval. These are the frequencies.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activities
The Basic Steps 1. Divide the range of the data values into consecutive intervals. 2. Define the end points of the intervals with one more decimal than used for the data set. 3. Count the number of data points that fall in each interval. These are the frequencies. 4. Construct a table (the frequency distribution table) showing the intervals and their frequencies.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activities
The Basic Steps 1. Divide the range of the data values into consecutive intervals. 2. Define the end points of the intervals with one more decimal than used for the data set. 3. Count the number of data points that fall in each interval. These are the frequencies. 4. Construct a table (the frequency distribution table) showing the intervals and their frequencies. 5. Enhance the table by showing the relative frequencies and the cumulative relative frequencies.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activities
Example (Life times (in thousands of cycles) of 100 aluminum strips subject to stress of 20,000 psi.)
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activities
Example (Life times (in thousands of cycles) of 100 aluminum strips subject to stress of 20,000 psi.) Class 1. 2. 3. 4. 5. 6. 7. 8.
350- Distribution, Select 3-parameter lognormal, OK, OK Try a different distribution: Right click on the fitted line> Select ”Edit distribution fit”>click on ”Options”> Choose 3-parameter gamma, OK, OK Copy and paste the two fitted histograms. Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
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Bar graphs and pie charts are used to depict the breakdown of a certain population into categories. Thus, they apply to qualitative or categorical data.
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For example, the ethnic, or religion composition, the education or income level of a certain population.
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Bar graphs resemble histograms in the sense of using bars to represent proportions, or counts, of the different categories.
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In a pie chart, the population is represented by a circle (pie) which is sliced up in pieces whose size represents proportions.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Example The site http://wardsauto.com/keydata/USSalesSummary0702.xls gives information on the light vehicle market share of car companies. The bar graph and pie chart below depict this data set.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Figure: Bar Graph of Light Vehicle Market Share Data.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
Figure: Pie Chart of Light Vehicle Market Share Data.
Michael Akritas
Lab8: Graphical Presentation of Data
Outline Box Plots Stem-and-Leaf Diagrams Histograms Bar Graphs and Pie Charts
Computer Activity
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Copy and paste the data from http: //www.stat.psu.edu/∼mga/401/Data/pie.data.txt
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Do a pie chart of this data using the commands: Graph>Pie Chart>Click on ”Chart counts of unique values”>Enter the data column>OK
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Type ”maybe” in rows 20-24 of the pie.data column in Minitab and try the above sequence again.
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Copy and paste the two graphs in the word document
Michael Akritas
Lab8: Graphical Presentation of Data
