Linear Transformations.  P. 89 39, 40,42,43  P. 97 45, 46.

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Presentation transcript:

Linear Transformations

 P , 40,42,43  P , 46

 Used to change scale  X new = b * x old + a  Very similar to y = mx + b  Issue: when we change scales how is the mean and standard deviation transformed?

PlayerSalary in Millions Shaquile O’Neal27.70 Eddie Jones13.46 Dwyane Wade2.83 Damon Jones2.50 Michael Doleac2.40 Rasual Butler1.20 Dorell Wright1.15 Qyntel Woods1.13 Christian Laettner1.10 Steve Smith1.10 Shandon Anderson.87 Keyon Dooling.75 Zhizhi Wang.62 Alonzo Mourning.33 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?

 If x old is transformed to x new = x old +a then:  1. Measures of center are increased by “a.”  2. Measures of spread remain unchanged.

 Suppose Instead that each player receives a 10% bonus. That is: X new = 1.1x 0ld 1. Enter this new data into your calculator 2. Compare the original and transformed measures of center and original and transformed measures of spread.

 If x old is transformed to x new = bx old then:  1. Measures of center are multiplied by b.  2. Measures of spread are multiplied by b.

 If x new = bx old +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.