Linear Transformations
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P. 89 39, 40 ,42 ,43
P. 97 45, 46
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Used to change scale
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Xnew = b * xold + a
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Very similar to y = mx + b
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Issue: when we change scales how is the
mean and standard deviation transformed?
1. Find the mean and
standard deviation
2. Report the five number
summary
3. Assume each player
receives a $100,000
signing bonus. What is
the new mean, standard
deviation and five
number summary?
Player
Salary in Millions
Shaquile O’Neal
27.70
Eddie Jones
13.46
Dwyane Wade
2.83
Damon Jones
2.50
Michael Doleac
2.40
Rasual Butler
1.20
Dorell Wright
1.15
Qyntel Woods
1.13
Christian Laettner
1.10
Steve Smith
1.10
Shandon
Anderson
.87
Keyon Dooling
.75
Zhizhi Wang
.62
Alonzo Mourning
.33
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If xold is transformed to xnew = xold +a then:
1. Measures of center are increased by “a.”
2. Measures of spread remain unchanged.
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Suppose Instead that each player receives a
10% bonus. That is:
Xnew = 1.1x0ld
1.
2.
Enter this new data into your calculator
Compare the original and transformed
measures of center and original and
transformed measures of spread.
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If xold is transformed to xnew = bxold then:
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1. Measures of center are multiplied by b.
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2. Measures of spread are multiplied by b.
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If xnew = bxold +a then:
1. Measures of center are multiplied by b AND
added to a.
2. Measures of spread are only multiplied by b

You measure temperature of 20 locations
within the pool and report your summary
statistics in degrees Fahrenheit. Your boss
wants the summary statistics in Celsius. Use
the linear transformation C = 5/9F – 160/9 to
explain how the mean, standard deviation,
and five number summary is easily
recalculated.