Section 1.2Day Two

Linear Transformations

P. 89 39, 40 ,42 ,43 P. 97 45, 46

Homework

Used to change scale

Xnew = b * xold + a

Very similar to y = mx + b

Issue: when we change scales how is the mean and standard deviation transformed?

Linear Transformations

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

Example1. 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?

If xold is transformed to xnew = xold +a then:

1. Measures of center are increased by “a.”

2. Measures of spread remain unchanged.

Linear Transformations

Suppose Instead that each player receives a 10% bonus. That is:

Xnew = 1.1x0ld

1. Enter this new data into your calculator2. Compare the original and transformed

measures of center and original and transformed measures of spread.

Example

If xold is transformed to xnew = bxold then:

1. Measures of center are multiplied by b.

2. Measures of spread are multiplied by b.

Linear Transformations

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

Putting it all together!

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.

Example