Box and Whisker Plots

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Box and Whisker Plots

• C. D. Toliver
• AP Statistics

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Percentile

• The percentile of a distribution of a set of data
  is a value such that p of the data fall at or
  below the data value and (100-p) of the data
  fall at or above it.
• Example 1 suppose you scored 2000 on your SAT
  and your score report said you fell in the 89th
  percentile. Then 89 of the test takers scored a
  2000 or less and 11 of the test takers scored
  2000 or more
• Example 2 The top 15 of the graduating class
  at WOS has a GPA of 3.9 or higher. That means
  they are at least in the 85th percentile. 85 of
  the students have a GPA of 3.9 or less.

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Quartiles

• Special percentiles (100 divided into fourths).
  So we consider data in the
• 25th percentile, quartile 1 (Q1)
• Median or 50th percentile, quartile 2 (Q2)
• 75th percentile, quartile 3 (Q3)

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How to Compute Quartiles

• Order the data from smallest to largest.
• Find the median. This is the second quartile, Q2.
• The first quartile Q1 is the median of the lower
  half of the data that is, it is the median of
  the data falling below Q2, but not including Q2
• The third quartile Q3 is the median of the upper
  half of the data that is, it is the median of
  the data falling above Q2 but not including Q2

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Example 1-Consider the data set10, 20, 30 40,
50, 60, 70

• The median, Q2 is 40
• Q1 is the median of the values below 40, These
  values are 10, 20, and 30. The median, or Q1 is
  20.
• Q3 is the median of the values above 40, These
  values are 50, 60 and 70 so the median or Q3 is
  60.

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Interquartile Range

• The interquartile range is the difference between
  Q3 and Q1 or Q3 Q1
• For our data set Q1 is 20, Q3 is 60, so the
  interquartile range is 60-20 40

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Five-Number Summary

• Lowest Value or minimum
• Q1
• Median
• Q3
• Highest value or maximum

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Five-Number Summary

• Example - For the data set 10,20,30,40,50,60,70
  
• The five number summary is
• Lowest number, 10
• Q1, 20
• Median, 40
• Q3, 60
• Highest number, 70

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Box and Whisker Plot

• A box and whisker plot is a graphical display of
  the five number summary
• Draw a scale to include the lowest and highest
  data values
• Draw a box from Q1 to Q3
• Include a solid line through the box at the
  median
• Draw solid lines, called whiskers from Q1 to the
  lowest value and from Q3 to the highest value.

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TI 84 1-Variable Stats
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TI 84 1-Variable Stats
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TI 84 1-Variable Stats
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TI 84 Box and Whisker Plot
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TI 84 Box and Whisker Plot
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TI 84 Box and Whisker Plot
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TI 84 Box and Whisker Plot
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TI 84 Box and Whisker Plot
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TI 84 Box and Whisker Plot
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Questions

• Is the median always in the middle of the box of
  your box and whiskers plot?
• How do outliers affect a box and whiskers plot?
• How can you use a box and whiskers plot to tell
  if your data is skewed right or skewed left?
• What would be a better way to display the data if
  you want to see the actual outliers?

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Example 2

• Compute the five-number summary and draw a box
  and whiskers plot for the test scores on a recent
  AP Statistics test
• 76, 59, 76, 78, 100,66,63,70,89,87,81,48,78
• What scores if any might be considered outliers?
• How do they affect the shape of the graph?
• How would the graph change if you removed the
  outliers?

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Example 3

• Compute the five-number summary and draw a box
  and whiskers plot for the test scores on a recent
  AP Statistics test in another class.
• 87,78,91,70,70,66,87,78,80,86,97,98,97,94
• What scores if any might be considered outliers?
• How do they affect the shape of the graph?
• How would the graph change if you removed the
  outliers?
• Compare the two sets of data? What can you
  conclude about the test results for the two
  classes?

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