Box-and-Whisker Plots

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Box-and-Whisker Plots
Box-and-Whisker Plots or Box Plots are useful for
showing the distribution of values in a data set.
The plot below is an example.
A consumer magazine rated 37 varieties of peanut
butter. Each peanut butter was assigned a quality
rating from 1-100 points. Peanut butters with a
higher quality ratings were smooth, had a
sweet-nutty flavor, and were not overly dry.
Peanut butters with lower quality ratings were
not very nutty, had small bits of peanuts, or had
a burnt or slightly rancid taste. Below is a
distribution of the ratings
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Step 1 Find the following values for the data
set.
Step 2 Construct a Box-and-Whisker Plot to
display the data.
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Interpreting the Data
25
25
25
25
The Box-and-Whisker Plot divides the data
distribution into 4 parts.
25 of the quality ratings for Natural Peanut
Butter were between 34 57.
25 of the quality ratings for Natural Peanut
Butter were between 57 61.5.
25 of the quality ratings for Natural Peanut
Butter were between 61.5 69.
25 of the quality ratings for Natural Peanut
Butter were between 69 89.
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You can compare distributions by displaying two
or more box plots on the same scale.
Of the 37 varieties of peanut butter, which type
had the higher quality ratings, Natural or
Regular?
Natural!
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Example 1
Fifteen shoppers rated a brand of paper towel on
a scale of 0 10. Their ratings were 2, 6, 6,
6, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, and 10.

• 1) Find the following
• Median
• Lower Quartile
• Upper Quartile
• Minimum rating
• Maximum rating
• Construct a Box-and-Whisker Plot to display the
  data.
• 3) Interpret the Data by describing the
  percentage breakdown of the paper towel ratings.

8 6 9 2 10
25 of the shoppers rated the paper towel between
2-6. 25 of the shoppers rated the paper towel
between 6-8. 25 of the shoppers rated the paper
towel between 8-9. 25 of the shoppers rated the
paper towel between 9-10.
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Example 2
Twenty students took a benchmark test. Their
scores were as follows 26, 52, 55, 55, 60, 61,
65, 68, 70, 70, 70, 72, 75, 79, 80, 84, 87, 90,
92, 95

• 1) Find the following
• Median
• Lower Quartile
• Upper Quartile
• Minimum rating
• Maximum rating
• Construct a Box-and-Whisker Plot to display the
  data.
• Interpret the Data by describing the percentage
  benchmark scores.

70 60 84 26 95
25 of the students scored between 26-60. 25 of
the students scored between 60-70. 25 of the
students scored between 70-84. 25 of the
students scored between 84-95