# Copyright 2005 Pearson Education, Inc. Slide 3-1 Chapter Copyright 2005 Pearson Education, Inc. Slide 3-1 Chapter 3 Copyright 2005 Pearson Education, Inc. Absolute Change vs. Relative Change absolute change 3-A = new value reference value = \$2,250 \$1,500 = \$750

relative change = absolute change reference value = new value reference value reference value = \$750 / \$1,500 = 50% Example: A diversified portfolio grows from \$1,500 to \$2,250. Copyright 2005 Pearson Education, Inc. Slide 3-3 3-A Absolute and Relative Difference

The absolute difference is the actual difference between the compared value and the reference value: absolute difference = compared value reference value The relative difference describes the size of the absolute difference as a fraction of the reference value: absolute difference relative difference = reference value compared value reference value reference value Copyright 2005 Pearson Education, Inc. Slide 3-4

Of versus More Than (or Less Than) Summary 3-A If the compared value is P% more than the reference value, it is (100 + P)% of the reference value. If the compared value is P% less than the reference value, it is (100 - P)% of the reference value. Copyright 2005 Pearson Education, Inc. Slide 3-5 3-A

Solving Percentage Problems Example: You purchase a shirt with a labeled (pre-tax) price of \$21. The local sales tax rate is 6%. What is your final cost (including tax)? final cost = labeled price + (6% of labeled price) = (100 + 6)% labeled price = 106% \$21 = 1.06 \$21 = \$22.26 Copyright 2005 Pearson Education, Inc. Slide 3-6 3-A

Abuses of Percentages Beware of Shifting Reference Values Less than Nothing Dont Average Percentages Copyright 2005 Pearson Education, Inc.

Slide 3-7 3-B Scientific Notation Scientific Notation is a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10. Examples: 6,700,000,000 in scientific notation is 6.7 109 0.000 000 000 000 002 is about 2.0 1015 Copyright 2005 Pearson Education, Inc.

Slide 3-8 3-B Selected Energy Comparisons Copyright 2005 Pearson Education, Inc. Slide 3-9 3-C Significant Digits Type of Digit Significance

Nonzero digit Always significant Zeros that follow a nonzero digit and lie to the right of the decimal point (as in 4.20 or 3.00) Always significant Zeros between nonzero digits (as in 4002 or 3.06) or other significant zeros (such as the first zero in 30.0) Always significant

Zeros to the left of the first nonzero digit Never significant (as in 0.006 or 0.00052) Zeros to the right of the last nonzero digit but before the decimal point as in (40,000 or 210) Copyright 2005 Pearson Education, Inc. Not significant unless stated otherwise Slide 3-10 3-C Two Types of Measurement Error Random errors occur because of random and

inherently unpredictable events in the measurement process. Systematic errors occur when there is a problem in the measurement system that affects all measurements in the same way, such as making them all too low or too high by the same amount. Copyright 2005 Pearson Education, Inc. Slide 3-11 3-C Absolute Error vs. Relative Error absolute error

= measured value true value = 25 billion 17 billion = 8 billion relative error = absolute error true value = measured value true value true value = 8 billion / 17 billion = 47.1% Example: A projected budget surplus of 17 billion turns out to be 25 billion at the end of the fiscal year. Copyright 2005 Pearson Education, Inc. Slide 3-12

3-C Accuracy vs. Precision Accuracy describes how closely a measurement approximates a true value. An accurate measurement is very close to the true value. Precision describes the amount of detail in a measurement. Copyright 2005 Pearson Education, Inc. Slide 3-13 3-D

Index Numbers An index number provides a simple way to compare measurements made at different times or in different places. The value at one particular time (or place) must be chosen as the reference value. The index number for any other time (or value index number = 100 reference value

place) is Copyright 2005 Pearson Education, Inc. Slide 3-14 3-D Consumer Price Index Copyright 2005 Pearson Education, Inc. Slide 3-15 Shaq, Vince and Simpsons Paradox

3-E Since Shaq has the better shooting percentages in both the first half and second half of the game, can he claim that he has the better game compared to Vince? Copyright 2005 Pearson Education, Inc. Slide 3-16 3-E Tree Diagram for Polygraphs Suppose that the polygraph is 90% accurate, how many of those applicants who were accused of lying were actually telling the

truth? Copyright 2005 Pearson Education, Inc. Slide 3-17 3-E Political Mathematics Republicans: Tax cut would benefit all families and the middle class would receive slightly greater benefits. Democrats: Tax cut would send disproportionate benefits to the rich. Which side was being more fair?

Copyright 2005 Pearson Education, Inc. Slide 3-18