1. The “Five-Number Summary” pictured in a Boxplot.
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2. We want to summarize the data
Don’t lose sight of the big picture here:
We have a data set
It’s a bunch of numbers
We want to summarize the data
Summarize means make it into a sound bite
We must be Concise – don’t say too much
We must be Informative – don’t say too little
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3. We must be Concise
Bad: “Here is a report that tells you the mean and the variance and the standard deviation and the quartiles and the percentiles from 0 to 100… and the marketing survey analyzed by demographic subgroups …” (there is a place for that, but not right now)
Good: “Got fifteen seconds? Here’s what we found.”
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4. We must be Informative “The mean is ________.” Not enough info.
“The median is ________.” Not enough info.
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5. The Five Number Summary strikes a balance
The Median in the middle
The Minimum and the Maximum at the extreme ends
Quartiles Q1 and Q3 to give an indication of spread and distribution of the data.
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6. Publisher’s slides
Here are a few slides from the Bluman 5th edition textbook:
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7. 3.4 Exploratory Data Analysis
The Five-Number Summary is composed of the following numbers: Low, Q1, MD, Q3, High
The Five-Number Summary can be graphically represented using a Boxplot.
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8. Constructing Boxplots
Procedure Table
Constructing Boxplots
Find the five-number summary.
Draw a horizontal axis with a scale that includes the maximum and minimum data values.
Draw a box with vertical sides through Q1 and Q3, and draw a vertical line though the median.
Draw a line from the minimum data value to the left side of the box and a line from the maximum data value to the right side of the box.
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9. Example 3-38: Meteorites
The number of meteorites found in 10 U.S. states is shown. Construct a boxplot for the data.
89, 47, 164, 296, 30, 215, 138, 78, 48, 39
30, 39, 47, 48, 78, 89, 138, 164, 215, 296
Five-Number Summary:
Low Q1 MD Q3
High 47
83.5
164 30
296
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10. Notice the pieces of the boxplot:
Horizontal scale, maybe a little beyond the min and the max. A generic number line.
The five numbers.
The box holds the quartiles
With a line in the middle at the median.
The whiskers extend out to the min and the max.
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11. TI-84 Boxplot
See instructions on separate handout.
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