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 xnew given by an
equation of the form
xnew = 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
Pages 59 – 61
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
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