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Boxplots. Lecture 17 Sec. 5.3.3 Wed, Feb 13, 2008. Boxplots. Boxplot – A graphical display of a five-number summary. Draw and label a scale representing the variable. Draw a box over the scale with its left and right ends at Q1 and Q3. Draw a vertical line through the box at the median.

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boxplots

Boxplots

Lecture 17

Sec. 5.3.3

Wed, Feb 13, 2008

boxplots2
Boxplots
  • Boxplot – A graphical display of a five-number summary.
    • Draw and label a scale representing the variable.
    • Draw a box over the scale with its left and right ends at Q1 and Q3.
    • Draw a vertical line through the box at the median.
    • Draw a left tail (whisker) from the box to the minimum.
    • Draw a right tail from the box to the maximum.
example
Example
  • Draw a boxplot of the sample

5, 20, 30, 45, 60, 80, 100, 140, 150, 200, 240.

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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boxplots and shape
Boxplots and Shape
  • What would a boxplot for a uniform distribution look like?
  • What would a boxplot for a symmetric distribution look like?
  • What would a boxplot for a right-skewed distribution look like?
ti 83 boxplots
TI-83 – Boxplots
  • Press STAT PLOT.
    • Select Plot1
      • Turn Plot 1 On.
      • Select the Boxplot Type.
      • Specify list L1.
  • Press ZOOM.
    • Select ZoomStat (#9) and press ENTER.
ti 83 boxplots13
TI-83 – Boxplots
  • Press TRACE.
    • Use the arrow keys to see the values of the minimum, Q1, the median, Q3, and the maximum.
modified boxplots
Modified Boxplots
  • Modified boxplot – A boxplot in which the outliers are indicated.
modified boxplots15
Modified Boxplots
  • Draw the box part of the boxplot as usual.
  • Compute STEP = 1.5  IQR.
  • The inner fences are at Q1 – STEP and Q3 + STEP.

Q1

Q3

modified boxplots16
Modified Boxplots
  • Draw the box part of the boxplot as usual.
  • Compute STEP = 1.5  IQR.
  • The inner fences are at Q1 – STEP and Q3 + STEP.

IQR

Q1

Q3

modified boxplots17
Modified Boxplots
  • Draw the box part of the boxplot as usual.
  • Compute STEP = 1.5  IQR.
  • The inner fences are at Q1 – STEP and Q3 + STEP.

1.5  IQR

1.5  IQR

IQR

Q1

Q3

modified boxplots18
Modified Boxplots
  • Draw the box part of the boxplot as usual.
  • Compute STEP = 1.5  IQR.
  • The inner fences are at Q1 – STEP and Q3 + STEP.

1.5  IQR

1.5  IQR

IQR

Upper

fence

Lower

fence

Q1

Q3

modified boxplots19
Modified Boxplots
  • Extend the whiskers from the box to the smallest and largest values that are within the inner fences.
  • Any values that are outside the inner fences should be drawn as individual dots. These dots represent outliers.
case study 8
Case Study 8
  • 2007 Small Arms Study (p. 47)
    • Find the five-number summary of the data.
    • Draw a modified boxplot.
box plots
Box Plots
  • For an example of modified boxplots, see DePaul University’s web page on retention.