Learn to find measures of variability'

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Learn to find measures of variability.
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Vocabulary
variability range quartile box-and-whisker plot
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The range of a data set is the largest value
minus the smallest value.
The table below summarizes a veterinarians
records for kitten litters born in a given year.
While central tendency describes the middle of a
data set, variability describes how spread out
the data is.
The range is affected by outliers, so another
measure is often used. Quartiles divide a data
set into four equal parts. The third quartile
minus the first quartile is the range for the
middle half of the data.
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The range of a data set is the largest value
minus the smallest value. For the kitten data,
the range is 6 2 4.
Kitten Data
Lower half
Upper half
2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5
5 6
The range is affected by outliers, so another
measure is often used. Quartiles divide a data
set into four equal parts. The third quartile
minus the first quartile is the range for the
middle half of the data.
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Additional Example 1A Finding Measures of
Variability
Find the range and the first and third quartiles
for the data set.
A. 15, 83, 75, 12, 19, 74, 21
Order the values.
12 15 19 21 74 75 83
range 83 12 71
first quartile 15
third quartile 75
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Additional Example 1B Finding Measures of
Variability
Find the range and the first and third quartiles
for the data set.
B. 75, 61, 88, 79, 79, 99, 63, 77
Order the values.
61 63 75 77 79 79 88 99
range 99 61 38
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Try This Example 1A
Find the range and the first and third quartiles
for the data set.
A. 25, 38, 66, 19, 91, 47, 13
Order the values.
13 19 25 38 47 66 91
range 91 13 78
first quartile 19
third quartile 66
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Try This Example 1B
Find the range and the first and third quartiles
for the data set.
B. 45, 31, 59, 49, 49, 69, 33, 47
Order the values.
31 33 45 47 49 49 59 69
range 69 31 38
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A box-and-whisker plot shows the distribution of
data. The middle half of the data is represented
by a box with a vertical line at the median.
The lower fourth and upper fourth quarters are
represented by whiskers that extend to the
smallest and largest values.
Median
First quartile
Third quartile
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Additional Example 2 Making a Box-and-Whisker
Plot
Use the given data to make a box-and-whisker
plot 21, 25, 15, 13, 17, 19, 19, 21
Step 1. Order the data and find the smallest
value, first quartile, median, third quartile,
and largest value.
13 15 17 19 19 21 21 25
smallest value 13
largest value 25
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Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 1. Order the data and find the smallest
value, first quartile, median, third quartile,
and largest value.
Step 2. Draw a number line and plot a point above
each value from step 1.
13 15 17 19 19 21 21 25
smallest value 13
first quartile 16
third quartile 21
median 19
largest value 25
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Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value.
Step 3. Draw the box and whiskers.
13 15 17 19 19 21 21 25
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Try This Example 2
Use the given data to make a box-and-whisker
plot. 31, 23, 33, 35, 26, 24, 31, 29
Step 1. Order the data and find the smallest
value, first quartile, median, third quartile,
and largest value.
23 24 26 29 31 31 33 35
smallest value 23
largest value 35
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Try This Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
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Try This Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
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Additional Example 3 Comparing Data Sets Using
Box-and-Whisker Plots
Note 57 is the first quartile and the median.
These box-and-whisker plots compare the ages of
the first ten U.S. presidents with the ages of
the last ten presidents (through George W. Bush)
when they took office.
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Additional Example 3 Continued
Note 57 is the first quartile and the median.
A. Compare the medians and ranges.
The median for the first ten presidents is
slightly greater. The range for the last ten
presidents is greater.
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Additional Example 3 Continued
Note 57 is the first quartile and the median.
B. Compare the differences between the third
quartile and first quartile for each.
The difference between the third quartile and
first quartile is the length of the box, which is
greater for the last ten presidents.
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Try This Example 3
These box-and-whisker plots compare the scores
per quarter at Super Bowl XXXVII. The data in the
T column is left out because it is a total of all
the quarters.
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Try This Example 3 Continued
A. Compare the medians and ranges.
The median for Tampa Bay is significantly
greater, however the range for Tampa Bay is
slightly greater.
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Try This Example 3 Continued
B. Compare the differences between the third
quartile and first quartile for each.
The difference between the third quartile and
first quartile is the length of the box, which is
slightly greater for Oakland.
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Lesson Quiz Part 1
Find the range and the first and third quartile
for each data set. 1. 48, 52, 68, 32, 53, 47,
51 2. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8,
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range 36 Q1 47 Q3 53
range 18 Q1 2.5 Q3 12
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Lesson Quiz Part 2
Use the following data for problems 3 and 4. 91,
87, 98, 93, 89, 78, 94 3. Make a
box-and-whisker plot 4. What is the mean?
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