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14
Descriptive Statistics
What a Data Set Tells Us
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section
Section14.3,
1.1, Slide
Slide11
14.3 Measures of Dispersion
• Compute the range of a data set.
• Understand how the standard
deviation measures the spread
of a distribution.
• Use the coefficient of variation to
compare the standard deviations
of different distributions.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 2
The Range of a Data Set
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 3
The Range of a Data Set
• Example: Find the range of the heights of the
people listed in the accompanying table.
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 4
Standard Deviation
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 5
Standard Deviation
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 6
Standard Deviation
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 7
Standard Deviation
• Example: A company has hired six interns.
After 4 months, their work records show the
following number of work days missed for each
worker:
0, 2, 1, 4, 2, 3
Find the standard deviation of this data set.
• Solution:
Mean:
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 8
Standard Deviation
We calculate the squares of the deviations of the
data values from the mean.
Standard Deviation:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 9
Standard Deviation
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 10
Standard Deviation
• Example: The following are the closing prices
for a stock for the past 20 trading sessions:
37, 39, 39, 40, 40, 38, 38, 39, 40, 41,
41, 39, 41, 42, 42, 44, 39, 40, 40, 41
What is the standard deviation for this data set?
• Solution:
Mean:
(sum of the closing prices is 800)
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 11
Standard Deviation
We create a table with values that will facilitate
computing the standard deviation.
Standard Deviation:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 12
Standard Deviation
Comparing Standard Deviations
All three distributions have a mean and median
of 5; however, as the spread of the distribution
increases, so does the standard deviation.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 13
The Coefficient of Variation
Relatively speaking there is more variation in the
weights of the 1st graders than the NFL players
below.
1st Graders
NFL Players
Mean: 30 pounds
Mean: 300 pounds
SD: 3 pounds
SD: 10 pounds
CV:
CV:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 14
The Coefficient of Variation
• Example: Use the coefficient of variation to
determine whether the women’s 100-meter race
or the men’s marathon has had more consistent
times over the five Olympics listed.
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 15
The Coefficient of Variation
• Solution:
100 Meters
Marathon
Mean: 10.796
Mean: 7,891.4
SD: 0.163
SD: 83.5
CV:
CV:
Using the coefficient of variation as a measure,
there is less variation in the times for the
marathon than for the 100-meter race.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.3, Slide 16
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