By: Amber Stanek

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Box and Whisker Plot

• By Amber Stanek

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What is a box and whisker plot?

• A box and whisker plot is a visual representation
  of how data is spread out and how much variation
  there is. It doesnt show all the data values,
  but instead focuses on the median, extremes, and
  quartiles.
• Lets see how Intermath defines a box and whisker
  plot.

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What are the median, extremes, and quartiles?
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Median

• The median is the middle value of an ordered set
  of numbers. (If the numbers are not in order
  from least to greatest, do this first!)
• Example 2 3 7 11 14
• In this case, the median is 7. (There are 2
  values below it and 2 values above it).
• Note If there is an even amount of data
  values, the median is found by adding the 2
  middle values together and then dividing that
  number by 2.
• Example 2 3 7 11 14 19
• In this case, you do the following 7 11
  18 (Youre adding the 2 middle values). Then
  you divide 18/2 9. The median is 9. (There
  are 3 numbers below 9 and 3 numbers above it.)

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Extremes

• The extremes are the highest and lowest values
  of the data set.
• Example 2 3 7 11 14
• In this case, the lower extreme is 2 and the
  upper extreme is 14.

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Quartiles

• The quartiles are the median of the higher half
  of the data set and the median of the lower half
  of the data set.
• Example 2 3 7 11 14
• In this case, the lower quartile is 2.5 (2
  3 55/2 2.5). The upper quartile is 12.5
  (11 14 2525/2 12.5).

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Lets Do an Example Together

• Well use the data we used when making a stem
  and leaf plot earlier the temperature every day
  for the month of August.

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Step 1

• There are 31 days in August, and here are the
  temperatures for that month
• August 76 82 83 90 93 85 78 75 71 71 72 69 70
  75 77 83 85 82 80 81 77 76 78 74 72 73 77 77
  76 77 72
• The first step is to take these data values and
  put them in order from least to greatest. -
  Example
• 69 70 71 71 72 72 72 73 74 75 75 76 76 76 77 77
  77 77 77 78 78 80 81 82 82 83 83 85 85 90 93

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Step 2

• The second step is to find the extremes.
  Remember, the lower extreme is the lowest value
  and the upper extreme is the highest value.
• -Example
• 69 70 71 71 72 72 72 73 74 75 75 76 76 76 77 77
  77 77 77 78 78 80 81 82 82 83 83 85 85 90 93
• Lower Extreme 69
• Upper Extreme 93

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Step 3

• The third step is to find the median. Remember,
  the median is the middle value.
• -Example
• 69 70 71 71 72 72 72 73 74 75 75 76 76 76 77 77
  77 77 77 78 78 80 81 82 82 83 83 85 85 90 93
• There are 31 values, therefore the median is
  the 16th value 77. (There are 15 values
  below it, and 15 values above it.)

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Step 4

• The fourth step is to find the lower quartile.
  Remember, this is the median of the lower half of
  the data.
• -Example
• 69 70 71 71 72 72 72 73 74 75 75 76 76 76 77
• There are 15 values therefore the median is
  the 8th value 73. (There are 7 values below
  it, and 7 values above it.)

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Step 5

• The fifth step is to find the upper quartile.
  Remember, this is the median of the upper half of
  the data.
• -Example
• 77 77 77 78 78 80 81 82 82 83 83 85 85 90 93
• There are 15 values therefore the median is
  the 8th value 82. (There are 7 values below
  it, and 7 values above it.)

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Step 6

• The sixth step is to plot the extremes (lower
  extreme 69, upper extreme 93), the quartiles
  (lower quartile 73 and upper quartile 82), and
  the median (77) on a number line.
• -Example

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Step 7

• The seventh step is to draw a rectangular box
  extending from the lower quartile to the upper
  quartile. Indicate the median with a vertical
  line extending through the box.
• -Example

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Step 8

• The eighth step is to connect the lower extreme
  to the lower quartile with a line (one "whisker")
  and the upper quartile to the upper extreme with
  another line (the other "whisker).
• -Example

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Completion!!!

• You have just finished your very own box and
  whisker plot! Congratulations! Remember to add
  a title and a key. Here is what your final
  product should look like
• Temperatures for August
• Key
• 75 75 degrees Fahrenheit

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What does the graph tell you?

• Well, you can see that the lowest temperature in
  August was 69 degrees Fahrenheit and the highest
  temperature was 93 degrees Fahrenheit. This
  gives you the range of the data 24. (93-69
  24)
• You also know that the median or middle value is
  77 degrees Fahrenheit.
• Since the medians (3 of them) represent the
  middle points, they split the data into 4 equal
  parts.
• One quarter of the data numbers are less than 73
• One quarter of the data numbers are between 73
  and 77
• One quarter of the data numbers are between 77
  and 82
• One quarter of the data numbers are greater than
  82

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A Special Case

• At some point you might see a box and whisker
  plot that has an asterisk like the example below.
  Sometimes there is one piece of data that falls
  way outside the range of the other values. This
  piece of data is called an outlier, and its
  shown by an asterisk in a box and whisker plot.
  If the outlier is included in the whisker, people
  might think that there are values dispersed
  throughout the whole range from the first
  quartile to the outlier. This would give them a
  false representation of the data.

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Another Example

• Would you like to see another example of a box
  and whisker plot? If so, click on the link
  below.
• Catching Fish in a Lake

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Practice What Youve Learned

• This is the end of the lesson, and now you have a
  chance to make a box and whisker plot of your
  own.
• Click on this link for the worksheet (written in
  pdf).
• Click on this link for the answers to the
  worksheet (written in pdf).

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Challenge

• Are you up for a challenge? If so, click on the
  following link and check your understanding of
  box and whisker plots.
• Assessment Questions