Download Standard Deviation

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