Medians, Quartiles and Box Plots

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Median, Quartiles, Inter-Quartile Range and Box
Plots.
Measures of Spread
Remember The range is the measure of spread
that goes with the mean.
Range 12 2 10
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Median, Quartiles, Inter-Quartile Range and Box
Plots.
Measures of Spread
The range is not a good measure of spread because
one extreme, (very high or very low value) can
have a big affect. The measure of spread that
goes with the median is called the inter-quartile
range and is generally a better measure of spread
because it is not affected by extreme values.
A reminder about the median
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Median drive 85 yards
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Median drive 90 yards
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Finding the median, quartiles and inter-quartile
range.
Example 1 Find the median and quartiles for the
data below.
12, 6, 4, 9, 8, 4, 9, 8,
5, 9, 8, 10
Order the data
4, 4, 5, 6, 8, 8, 8, 9,
9, 9, 10, 12
Inter-Quartile Range 9 - 5½ 3½
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Finding the median, quartiles and inter-quartile
range.
Example 2 Find the median and quartiles for the
data below.
6, 3, 9, 8, 4, 10, 8,
4, 15, 8, 10
Order the data
3, 4, 4, 6, 8, 8, 8, 9,
10, 10, 15,
Inter-Quartile Range 10 - 4 6
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The averages are similar but the measures of
spread are significantly different since the
extreme values of 2 and 15 are not included in
the inter-quartile range.
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Box Plots
Lower Quartile
Upper Quartile
Lowest Value
Highest Value
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CFC
Box Plot from Cumulative Frequency Curve
We can now construct a partial box plot from our
earlier work on cumulative frequency curves.
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Worksheet 1
worksheet
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Worksheet 2
worksheet
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