Statistical Graphs for 1 Variable Dotplot Histogram Boxplot

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Statistical Graphs for 1 VariableDotplotHistogr
amBoxplot
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Dotplot

• This dotplot depicts a right skewed distribution
  (distribution means pattern of variation). For
  such a distribution values below the median (here
  M 29.17) tend to be closer together than those
  above. We say Fruit flies longevities have a
  right skewed distribution.

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Histogram

• Rules for constructing histograms are provided in
  the text.

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Histogram Variations
Frequency Histogram
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Histogram Variations
Relative Frequency Histogram
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Histogram Variations
Class endpoints Every other omitted
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Histogram Variations
Class midpoints Every other omitted
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Histogram Shapes

• Right Skewed

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Histogram Shapes

• Right Skewed

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Histogram Shapes

• Very Right Skewed

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Histogram Shapes

• Somewhat Right Skewed

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Histogram Shapes

• Left Skewed

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Histogram Shapes

• Symmetric Normal

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Histogram Shapes

• Symmetric (Not Normal)

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Histogram Shapes

• Uniform

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Histogram Shapes

• Multimodal (Bimodal)

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Histogram

• We speak of the general shape of a histogram we
  dont pay too much attention to the particulars.
• Every shape goes along with a particular pattern
  among percentiles.

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Boxplots the 5 Summary

• To construct a boxplot, first obtain the 5 number
  summary
• Min, Q1, M, Q3, Max
• Q1 1st quartile 25th percentile
• M Q2 median 2nd quartile 50th percentile
• Q3 3rd quartile 75th percentile

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Example Simple Boxplot

• Failure times of industrial machines (in hours)
• 32.56 42.02 47.26 50.25 59.03
  60.17 61.56 62.16 62.84 63.29
  63.52 65.52 66.54 68.71 70.60
  71.27 76.33 80.37 82.87
• 5 summary
• 32.56 , 59.03 , 63.29 , 70.60 , 82.87

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Example Simple Boxplot

• 32.56 , 59.03 , 63.29 , 70.60 , 82.87
• Line at median.

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Example Simple Boxplot

• 32.56 , 59.03 , 63.29 , 70.60 , 82.87
• Box to quartiles.

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Example Simple Boxplot

• 32.56 , 59.03 , 63.29 , 70.60 , 82.87
• Whiskers/Fences to extremes.

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Example Simple Boxplot

• The final product A Simple Boxplot.
• Only quartile information is displayed.
• Other percentiles can be interpolated. This will
  tend to give rough approximations.

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Example Modified Boxplot

• A mathematical rule designates outliers. These
  are plotted using special symbols.
• (Note The minimum is still 32.56.)

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Modified Boxplot Outliers

• A mathematical rule designates outliers.
• Outliers are part of the data do not assume
  they are bad data or can be deleted. In fact,
  they may constitute the most meaningful
  information in the data.
• If we discover why the one machine failed so
  early, perhaps we can adjust to prevent early
  failure for future machines.
• Then future failure times should be plotted in a
  new boxplot.

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Modified Boxplot Outliers

• A mathematical rule designates outliers.
• Sometimes an outlier is ripe for
• change
• learn why its wrong and correct it
• deletion
• determine why its different and doesnt belong

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Modified Boxplot Outliers

• A mathematical rule designates outliers.
• For a large set of good data drawn from a Normal
  population, about 2 of the data will be marked
  outlier in a modified boxplot.
• For small but good data sets, generally more than
  2 will be so marked.
• For good data from skewed distributions,
  generally much more than 2 will be so marked.

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Modified Boxplot Outliers

• Learn to match shape with boxplot orientation.