Box and Whisker Plots
C. D. Toliver
AP Statistics
Percentile
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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.
Quartiles
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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
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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
Example 1-Consider the data set:
{10, 20, 30 40, 50, 60, 70}
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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.
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
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Lowest Value or minimum
Q1
Median
Q3
Highest value or maximum
Five-Number Summary
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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
TI 84 1-Variable Stats
TI 84 1-Variable Stats
TI 84 Box and Whisker Plot
TI 84 Box and Whisker Plot
TI 84 Box and Whisker Plot
TI 84 Box and Whisker Plot
TI 84 Box and Whisker Plot
TI 84 Box and Whisker Plot
Questions
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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?
Example 2
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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?
Example 3
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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?