Box Plots and Outliers

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Box Plots and Outliers
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Box Plot

• We need 5 numbers, called the 5 number summary
• 1. minimum value
• 2. Q1
• 3. median
• 4. Q3
• 5. maximum value

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Harry Potter Data

• The 5 number summary is
• Minimum 70.9
• Q1 78.9
• Median 81.35
• Q3 84.45
• Maximum 86.2

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Drawing the plot free hand

• Use a scaled line to draw the box plot
• Approximate locations of the values.
• We say this is SKEWED LEFT since the longer tail
  is on the left side.

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Using the TI

• Put the data into the list
• Press y make sure that there is nothing in
  the 10 equations

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• Press 2nd key, y
• There are 3 statistical plots.
• Press 1

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• Turn the plot ON
• Select the 2nd box plot
• Make the x list L1

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• Press Zoom
• Press Enter on 9

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• The Box plot will appear

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• Press TRACE to see values use right or left
  arrow keys to move around.

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Inter-quartile Range

• The inter-quartile range (IQR) is the value of Q3
  Q1

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Outliers

• An outlier is an unusual score, relative to the
  data set. It will influence the mean and the
  standard deviation.
• A data set might have no outliers, one outlier,
  or several outliers.
• Two types Mild and Extreme

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Mild Outliers

• Look for data values (x) that are either
• 1.
• 2.

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Extreme Outliers

• Look for values that are either
• 1.
• 2.

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Harry Potter data - checking
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Example Ages of actresses at the time they first
won the Oscar
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5 number summary for actresses

• Min 21
• Q1 30
• Med 34
• Q3 41
• Max 80

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Actresses

• Check for outliers. Identify type.

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Box plot with outliers

• When we select the 1st box plot on the TI, it
  allows us to see outliers. Select the mark that
  is visible for you.

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• Zoom 9 results in

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• Trace and go to the right twice.
• The 50 is the last data value that is not an
  outlier.

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Comparison of Boxplots and histograms