Copyright © 2005 Pearson Education, Inc. Slide 3-1.

Copyright © 2005 Pearson Education, Inc. Slide 3-1

Copyright © 2005 Pearson Education, Inc.

Chapter 3


Absolute Change vs. Relative Change

3-A

absolute change

relative change

Example: A diversified portfolio grows from $1,500 to $2,250.

= new value – reference value

= $2,250 – $1,500 = $750

absolute change= reference value

new value reference value= reference value

= $750 / $1,500 = 50%


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:

3-A

absolute differencerelative difference =

reference valuecompared value reference value

reference value


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.


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

3-A


Abuses of Percentages

Beware of Shifting Reference Values

Less than Nothing

Don’t Average Percentages

3-A


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

3-B


Selected Energy Comparisons

3-B


Significant Digits

3-C

Not significant unless stated otherwiseZeros to the right of the last nonzero digit but before the decimal point as in (40,000 or 210)

Never significantZeros to the left of the first nonzero digit (as in 0.006 or 0.00052)

Always significantZeros between nonzero digits (as in 4002 or 3.06) or other significant zeros (such as the first zero in 30.0)

Always significantZeros that follow a nonzero digit and lie to the right of the decimal point (as in 4.20 or 3.00)

Always significantNonzero digit

SignificanceType of Digit


Two Types of Measurement Error

3-C

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.


Absolute Error vs. Relative Error

3-C

absolute error = measured value – true value

Example: A projected budget surplus of 17 billion turns

out to be 25 billion at the end of the fiscal year.

= 25 billion – 17 billion = 8 billion

absolute error= true value

measured value true value= true value

= 8 billion / 17 billion = 47.1%

relative error


Accuracy vs. Precision

3-C

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.


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

place) is

3-D

value

index number = 100reference value


Consumer Price Index

3-D


Shaq, Vince and Simpson’s 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?


Tree Diagram for Polygraphs

3-E

Suppose that the polygraph is 90% accurate, how many of those applicants who were accused of lying were actually telling the truth?


Political Mathematics

3-E

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 3-1.

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