Chapter 3 Numerically Summarizing Data

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Chapter 3Numerically Summarizing Data

• Section 3.5
• Five Number Summary Boxplots

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The Five-Number Summary MINIMUM Q1 M Q3 MAXIMUM
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EXAMPLE Finding the Five Number Summary
Find the five number summary for the employment
ratio data from Section 3.4.
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Steps for Drawing a Boxplot
Step 1 Determine the lower and upper fence
Lower Fence Q1 - 1.5(IQR) Upper Fence Q3
1.5(IQR)
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Steps for Drawing a Boxplot
Step 1 Determine the lower and upper fence
Lower Fence Q1 - 1.5(IQR) Upper Fence Q3
1.5(IQR) Step 2 Draw vertical lines at Q1, M,
and Q3. Enclose these vertical lines in a box.
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Steps for Drawing a Boxplot
Step 1 Determine the lower and upper fence
Lower Fence Q1 - 1.5(IQR) Upper Fence Q3
1.5(IQR) Step 2 Draw vertical lines at Q1, M,
and Q3. Enclose these vertical lines in a box.
Step 3 Label the lower and upper fence.
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Steps for Drawing a Boxplot
Step 1 Determine the lower and upper fence
Lower Fence Q1 - 1.5(IQR) Upper Fence Q3
1.5(IQR) Step 2 Draw vertical lines at Q1, M,
and Q3. Enclose these vertical lines in a box.
Step 3 Label the lower and upper fence. Step 4
Draw a line from Q1 to the smallest data value
that is larger than the lower fence. Draw a line
from Q3 to the largest data value that is smaller
than the upper fence.
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Steps for Drawing a Boxplot
Step 1 Determine the lower and upper fence
Lower Fence Q1 - 1.5(IQR) Upper Fence Q3
1.5(IQR) Step 2 Draw vertical lines at Q1, M,
and Q3. Enclose these vertical lines in a box.
Step 3 Label the lower and upper fence. Step 4
Draw a line from Q1 to the smallest data value
that is larger than the lower fence. Draw a line
from Q3 to the largest data value that is smaller
than the upper fence. Step 5 Any data values
less than the lower fence or greater than the
upper fence are outliers and are marked with an
asterisk ().
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EXAMPLE Drawing a Boxplot Draw a boxplot for
the employment ratio data.
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Distribution Shape Based Upon Boxplot
1. If the median is near the center of the box
and each of the horizontal lines are
approximately equal length, then the distribution
is roughly symmetric. 2. If the median is left of
the center of the box and/or the right line is
substantially longer than the left line, the
distribution is right skewed. 3. If the median is
right of the center of the box and/or the left
line is substantially longer than the right line,
the distribution is left skewed
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Symmetric
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Skewed Right
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Skewed Left
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EXAMPLE Identify the Shape of a Distribution
from a Boxplot Determine the shape of the
employment ratio data based on the boxplot.
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EXAMPLE Comparing Two Data Sets Using
Boxplots
The following data represent the birth rate for
women 15 - 44 years of age in 1990 and 1997 for
each state. Draw boxplots for each year using
the same scale.
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60.5 63.9 68.0 66.1 64.8 74.2 85.3 64.1 65.9 66.1
64.7 67.3 67.4 86.3 60.5 66.5 73.8 56.1 72.9 65.9
79.2 62.4 73.0 69.1 65.5 70.1 77.7 63.6 69.4 70.3
69.7 72.1 82.3 64.2 64.7 68.9 69.7 67.5 92.0 69
.1 66.3 67.2 71.5 77.2 77.6 67.0 64.8 71.7 62.8 6
5.9 68.7
1990
49.5 68.4 60.3 61.2 64.2 55.9 61.8 52.4 60.0 58.9
62.1 70.4 60.7 69.0 49.6 58.1 61.7 66.3 78.1 62.9
72.4 57.8 61.4 58.0 67.3 88.5 64.6 56.6 60.4 53.1
65.7 75.4 65.7 60.3 62.2 64.3 67.8 61.8 64.9 63
.9 61.0 60.4 75.3 62.7 59.9 64.1 63.6 66.1 59.1 7
2.3 70.3
1997
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