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Quantitative Wisdom:
Numerical literacy from the perspective of Biblical wisdom
Dr. Ryan Johnson
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Front Matter
Author Biography
Dedication
Acknowledgements
Colophon
1
Introduction
1.1
Time Management Lab
1.1.1
Rule of 60
1.1.2
Master Calendar
1.1.3
Schedule
1.1.4
20 Tips for Managing Your Time
1.2
Mindset Lab
1.3
God and Math
2
Numbers
2.1
Problem Solving
2.2
Orders of Magnitude
2.3
Proportional Reasoning
2.4
Unit Conversion
2.4.1
Equivalences Table
2.4.2
Metric Prefixes
2.4.3
Rates
2.4.4
Using Dimensional Analysis for Area and Volume units
2.5
Cost of Driving
2.6
Home Improvements
2.7
Percentages
3
Finance
3.1
Introduction to Spreadsheets
3.1.1
Basic Calculations
3.1.2
Cell References
3.1.3
Cell Formatting
3.1.4
Fill-Down Feature
3.1.5
Formulas
3.1.6
Using a Spreadsheet for a Personal Budget
3.1.7
Exercises
3.2
Simple and Compound Interest
3.2.1
Simple Interest
3.2.2
APR – Annual Percentage Rate
3.2.3
Compound Interest
3.2.4
The Future Value Spreadsheet Formula
3.2.5
Comparing Simple and Compound Interest
3.2.6
Finding the Principal, or Present Value
3.2.7
The Present Value Spreadsheet Formula
3.2.8
Continuously Compounded Interest
3.2.9
Finding the Amount of Interest Earned and the Percentage
3.2.10
Effective Rate
3.2.11
Exercises
3.3
Savings Plans
3.3.1
Warmup
3.3.2
Savings Plan Formulas
3.3.3
Finding Payment Amounts Usings Spreadsheets and Formulas
3.3.4
Comparing Lump Sum and Regular Savings Payments
3.3.5
Deriving the Savings Plan Formula (Optional)
3.3.6
Exercises
3.4
Loan Payments
3.4.1
Installment Loans
3.4.2
Loan Formulas
3.4.3
Remaining Loan Balance
3.4.4
Credit Cards
3.4.5
Summary of Spreadsheet Formulas
3.4.6
When to use the formulas: What is the question asking?
3.4.7
Summary of Mathematical Formulas
3.4.8
When to use the formulas: What is the question asking?
3.4.9
Exercises
3.5
Income Taxes
3.5.1
A Very Brief History of Taxes
3.5.2
Types of Income Tax
3.5.3
Federal Income Tax
3.5.4
State Income Tax
3.5.5
Municipal Income Tax
3.5.6
Calculating Federal Income Tax
3.5.7
Gross Income
3.5.8
Adjusted Gross Income
3.5.9
Taxable Income
3.5.10
Filing Status
3.5.11
Tax Tables
3.5.12
Tax Credits
3.5.13
Calculating a Refund or Payment Due
3.5.14
Exercises
3.6
Planning and Budget Project
3.6.1
Details
3.6.2
Assignment
3.6.3
Grading Break Down
4
Data
4.1
Overview of the Statistical Process
4.1.1
Statistical Process
4.1.2
Population
4.1.3
Parameter
4.1.4
Sample
4.1.5
Statistic
4.1.6
Sampling
4.1.7
Sampling Methods
4.1.8
Simple random sample (SRS)
4.1.9
Stratified sampling
4.1.10
Systematic sampling
4.1.11
Convenience sampling
4.1.12
Statistical Bias
4.1.13
Types of bias
4.1.14
Observational Studies
4.1.15
Experiments
4.1.16
Confounding
4.1.17
Control group
4.1.18
Placebo effect
4.1.19
Placebo and Placebo-controlled experiments
4.1.20
Blind studies
4.1.21
Margin of Error and Confidence Intervals
4.1.22
Exercises
4.2
Describing Data
4.2.1
Types of Data
4.2.2
Presenting Categorical Data
4.2.3
Frequency Tables
4.2.4
Relative Frequency Tables
4.2.5
Bar graphs
4.2.6
Pie Charts
4.2.7
Using a Spreadsheet to Make Bar Charts and Pie Charts
4.2.8
Misleading Graphs
4.2.9
Perceptual Distortion
4.2.10
Misleading Scale
4.2.11
Stacked Bar Graphs
4.2.12
Presenting Quantitative Data
4.2.13
Histograms
4.2.14
Class Intervals
4.2.15
Histograms Using Technology
4.2.16
The Shape of a Distribution
4.2.17
Modality
4.2.18
Symmetry
4.2.19
Skewness
4.2.20
Skewed to the Left
4.2.21
Skewed to the Right
4.2.22
The Normal Distribution
4.2.23
Outlier
4.2.24
Exercises
4.3
Summary Statistics: Measures of Center
4.3.1
Calculating Summary Statistics
4.3.2
Measures of Center
4.3.3
Mode
4.3.4
Mean
4.3.5
Median
4.3.6
The Relationship Between the Mean and the Median
4.3.7
Exercises
4.4
Summary Statistics: Measures of Variation
4.4.1
Measures of Variation
4.4.2
Standard Deviation
4.4.3
Range
4.4.4
Quartiles and the Interquartile Range
4.4.5
The Five-Number Summary and Boxplots
4.4.6
Modified Boxplot (Optional)
4.4.7
Percentiles
4.4.8
Comparing Distributions
4.4.9
Z-Scores
4.4.10
Exercises
5
Math Models
5.1
Function Notation and Linear Functions
5.1.1
What is a Function?
5.1.2
Math as a Language
5.1.3
The Grammar of Function Notation
5.1.4
Average Rate of Change, Inuitive Knowledge
5.1.5
Three Representations of a Relationship
5.1.6
Linear Equations and Slope
5.1.7
Slope Intercept Equation of a Line
5.1.8
Exercises
5.2
Exponential Growth and Decay
5.2.1
Exponential Growth
5.2.2
Growth Factors
5.2.3
Percent Increase
5.2.4
Exponential Decay
5.2.5
Decay Factors
5.2.6
Comparing Linear Growth and Exponential Growth
5.2.7
Exercises
5.3
Exponential Models
5.3.1
Fitting an Exponential Function through Two Points
5.3.2
Doubling Time
5.3.3
Half-Life
5.3.4
Homework 4.5
5.4
Periodic Functions
5.5
Carbon Dioxide Lab
5.5
6
Democracy
6.1
Apportionment
6.1.1
Historical Context for This Chapter
6.1.2
What is Apportionment?
6.1.3
Hamilton’s Method
6.1.4
Problems with Hamilton’s Method
6.1.5
Jefferson’s Method
6.1.6
Webster’s Method
6.1.7
Land Rights, Citizenship and Voting Rights
6.1.8
Huntington-Hill Method
6.1.9
What is the Geometric Mean?
6.1.10
Exercises
6.2
Voting Methods
6.2.1
Voting Rights
6.2.2
Ranked Choice Ballots
6.2.3
Preference Schedule
6.2.4
Plurality Method
6.2.5
How Many Votes are Needed to Win?
6.2.6
Insincere Voting
6.2.7
Instant Runoff Method
6.2.8
Borda Count (Point System)
6.2.9
Pairwise Comparison: Copeland’s Method
6.2.10
Which Method is the Most Fair?
6.2.11
Primaries and Sequential Voting
6.2.12
Exercises
6.3
The Popular Vote, Electoral College and Electoral Power
6.3.1
Choosing the U.S. President
6.3.2
How Electoral Votes are Determined
6.3.3
Electoral Power
6.3.4
Exercises
6.4
Gerrymandering and How to Measure It
6.4.1
Forming State Legislative Districts
6.4.2
Proportionality and Fairness
6.4.3
How to Gerrymander
6.4.4
The Efficiency Gap
6.4.5
Exercises
Back Matter
A
Selected Hints
B
Solutions to Odd Exercises
Index
Colophon
Colophon
Colophon
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