Box Plots

1
Box Plots

• S1 Representing Data

2
Why use a Box Plot

• To see how the data are spread
• To compare 2 or more data sets

3
Box Plot 5 Number Summary
Lowest value
Highest value
Lower Quartile Q1
Upper Quartile Q3
Median Q2
4
Calculating Quartiles

• As with Stem Leaf diagrams
• Q2 - MEDIAN
• Calculate as the Middle Value
• Q1 Lower Quartile
• ¼ n th value
• Q3 Upper Quartile
• ¾ n th value

5
Example

• For n 50 values
• Q1 ¼ x 50th value 12½th 13th
• Q2 ½(501)th 25½th value
• Q3 ¾ x 50th value 37½th 38th

6
Plotting the graph
20 30 40 50 60
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Analysis - Skew
25 of data in EACH Quartile
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SYMMETRICAL DISTRIBUTION
Q2 - Q1 Q3 Q2
MEAN MEDIAN MODE
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POSITIVELY SKEWED DISTRIBUTION
Q2 - Q1 lt Q3 Q2
MEAN gt MEDIAN gt MODE
10
NEGATIVELY SKEWED DISTRIBUTION
Q2 - Q1 gt Q3 Q2
MEAN lt MEDIAN lt MODE
11
Outliers

• OUTLIERS are values in the data set that lie
  OUTSIDE a defined Upper and/or Lower value
• These values are called FENCES
• FENCES are defined as
• Lower is Q1 1.5 x IQR
• Upper is Q3 1.5 x IQR

12
Fences and Outliers
Plot any OUTLIER as a X
20 30 40 50 60
70 80 90 100 110
minutes
Lower Fence 29 1½ x (57-29) -13 No Fence!
Upper Fence 57 1½ x (57-29) 99 Draw WHISKER
to the FENCE!