AP STATISTICS LESSON 1 – 2 (DAY 3) LINEAR TRANSFORMATIONS AND COMPARING DISTRIBUTIONS

ESSENTIAL QUESTION: How is the shape and spread effected by linear transformations? Objective: To transform data and find the effect on the shape and spread.

Linear Transformation A linear transformation changes the original variable x into the new variable x new given by an equation of the form x new = a + bx Adding the constant a shifts all values of x upward or downward by the same amount. Multiplying by the positive constant b changes the size of the unit of measurement.

Exercise: Page 53 Example 1.15 LOS ANGELES LAKERS’ SALARIES

Effects of Linear Transformation To see the effect of a linear transformation on measures of center and spread, apply these rules: Multiplying each observation by a positive number b multiplies both measures of center (mean and median) and measures of spread ( standard deviation and IQR) by b. Adding the same number a ( either positive or negative to each observation adds a to measures of center and to quartiles but does not change measures of spread.

Exercises 1.47: Get Your Hot Dogs Here! Exercise 1.48: Which AP Exam is Easier: Calculus AB or Statistics? Exercise 1.49: Who Makes More? Exercise 1.50: Basketball Playoff Scores Exercises Pages 59 – 61

Page 57 Example 1.17 Swiss Doctors Male doctors: 27, 50, 33, 25, 86, 25, 86, 25, 85, 31, 37, 44, 20, 36, 59, 34, 28 Female doctors: 5, 7, 10, 14, 18, 19, 25, 29, 31, 33