Download Standard Deviation

Dr. Fowler  AFM  Unit 8-3
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.
Write all Notes – All slides today – notes are short
• Example: Find the range of the heights of the people listed
in the accompanying table.
Solution:
Standard Deviation:
https://www.youtube.com/watch?v=09kiX3p5Vek
Standard Deviation
Standard Deviation
Standard Deviation
Section 15.3, Slide 7
Standard Deviation
Section 15.3, Slide 8
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 step 1:
Mean:
(sum of the closing prices is 800)
(continued on next slide)
Section 15.3, Slide 9
Standard Deviation
We create a table with values that will facilitate computing the
standard deviation.
Standard Deviation:
The Coefficient of Variation
Relatively speaking there is more variation in the weights of
the 1st graders than the NFL players below.
1st Graders
Mean: 30 pounds
SD: 3 pounds
CV:
NFL Players
Mean: 300 pounds
SD: 10 pounds
CV:
Section 15.3, Slide 11
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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)
Section 15.3, Slide 14
Standard Deviation
We calculate the squares of the deviations of the
data values from the mean.
Standard Deviation:
Section 15.3, Slide 15
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)
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.
Section 15.3, Slide 17
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.
Section 15.3, Slide 18