Boxplots

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# Boxplots - PowerPoint PPT Presentation

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

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.
• Draw a left tail (whisker) from the box to the minimum.
• Draw a right tail from the box to the maximum.
Example
• Draw a boxplot of the sample

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

Example

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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
• 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 – Boxplots
• Press TRACE.
• Use the arrow keys to see the values of the minimum, Q1, the median, Q3, and the maximum.
Modified Boxplots
• Modified boxplot – A boxplot in which the outliers are indicated.
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 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 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 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 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
• 2007 Small Arms Study (p. 47)
• Find the five-number summary of the data.
• Draw a modified boxplot.
Box Plots
• For an example of modified boxplots, see DePaul University’s web page on retention.