Download presentation

Presentation is loading. Please wait.

1
**Changing the unit of measurement**

AP Statistics

2
**Linear transformation**

A linear transformation changes the original variable x into a new variable given by an equation of the form 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

3
**Effect of a linear transformation**

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

4
**How much will the mean salary increase? The median salary? **

Page A school system employs teachers at salaries between $30000 and $ The teacher’s union and the school board are negotiating the form of next year’s increase in the salary schedule. Suppose that every teacher is given a flat $1000 raise. How much will the mean salary increase? The median salary? The mean and the median will both increase by 1000 Will a flat $1000 raise increase the spread as measured by the distance between the quartiles? No. Each Quartile will increase by 1000 therefore the difference will remain the same Will a flat $1000 raise increase the spread as measured by the standard deviation of the salaries? No, the standard deviation remains unchanged when the same amount is added to each data value

5
Page 56 #1.46 Suppose that the teachers in the previous exercise each receive a 5% raise. The amount of the raise will vary from $1500 to $3000, depending on present salary. Will a 5% raise across-the-board increase the spread of the distribution as measured by the distance between the quartiles? Do you think it will increase the standard deviation? A 5% across-the –board raise will cause both the IQR and s to increase. The transformation being applied here is , where x = the old salary and = the new salary. Both IQR and s will increase by a factor of 1.05

Similar presentations

OK

+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 6: Random Variables Section 6.2 Transforming and Combining Random Variables.

+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 6: Random Variables Section 6.2 Transforming and Combining Random Variables.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on enterprise resource planning Ppt on introduction to object oriented programming Ppt on low level language list Ppt on life insurance in india Download ppt on modern farming methods Ppt on applied operations research va Ppt on sbi mutual fund Lecture ppt on digital image processing Ppt on power sharing in indian and other countries Maths ppt on binomial theorem