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Elementary Statistics Supplementary Notes
David W. Lyons
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\( \DeclareMathOperator{\AVE}{AVE} \DeclareMathOperator{\SUM}{SUM} \DeclareMathOperator{\SD}{SD} \DeclareMathOperator{\rms}{rms} \DeclareMathOperator{\REGR}{REGR} \DeclareMathOperator{\AND}{AND} \DeclareMathOperator{\OR}{OR} \DeclareMathOperator{\OPPOSITE}{OPPOSITE} \DeclareMathOperator{\Inn}{Inn} \DeclareMathOperator{\lcm}{lcm} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\Perm}{Perm} \DeclareMathOperator{\Stab}{Stab} \DeclareMathOperator{\Orb}{Orb} \DeclareMathOperator{\Rot}{Rot} \DeclareMathOperator{\re}{Re} \DeclareMathOperator{\im}{Im} \DeclareMathOperator{\img}{image} \DeclareMathOperator{\conj}{conj} \DeclareMathOperator{\Id}{Id} \newcommand{\C}{\mathbb{C}} \newcommand{\Quat}{\mathbb{H}} \newcommand{\extC}{\hat{\C}} \newcommand{\R}{\mathbb{R}} \newcommand{\extR}{\hat{\R}} \newcommand{\F}{\mathbb{F}} \newcommand{\extF}{\hat{\F}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Proj}{\mathbb{P}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\M}{{\rm \bf M}} \newcommand{\E}{{\rm \bf E}} \renewcommand{\H}{{\rm \bf H}} \newcommand{\HU}{\H_{\U}} \renewcommand{\S}{{\rm \bf S}} \newcommand{\D}{\mathbb{D}} \newcommand{\closedD}{\hat{\D}} \newcommand{\U}{\mathbb{U}} \newcommand{\spacer}{\rule[0cm]{0cm}{0cm}} \newcommand{\MOD}{\mathbin{\text{MOD}}} \newcommand{\twotwo}[4]{\left[ \begin{array}{cc} #1 \amp #2 \\ #3 \amp #4 \end{array} \right]} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Preface
1
Commentary and Skills
1.1
General
1.1.1
Rounding in calculations
1.1.2
Solving equations
1.1.3
Solving equations practice problems
1.2
Histograms
1.2.1
Examples
1.2.2
Percentile
1.2.3
Histogram practice problems
1.2.3
Exercises
1.3
Displacement, deviation
1.3.1
Displacement, Deviation
1.4
Normal Distributions
1.4.1
Using the Normal Table
1.4.2
Examples
1.4.3
Normal curve practice problems (Ch 5)
1.4.3
Exercises
1.5
Lines: Slope, Rise, and Run
1.5.1
Basics for lines
1.5.2
Practice problems for lines
1.6
Regression
1.6.1
Terminology: the term "football-shaped"
1.6.2
Examples
1.6.3
Regression practice problems
1.6.3
Exercises
1.7
Probability
1.7.1
Probability terminology (Ch 13–15)
1.7.2
Probability Practice Problems
1.7.2
Exercises
1.8
Sampling
1.8.1
The Law of Averages (Ch 16,17)
1.8.2
A special case SD formula (Ch 17)
1.8.3
Sum of Draws Practice Problems (Ch 16–18)
1.8.3
Exercises
2
Summary Notes
2.1
Descriptive Statistics
2.1.1
The Histogram
2.1.2
Average, Median, Percentiles
2.1.3
Operations on Lists
2.1.4
Standard Deviation and Standard Units
2.1.5
The Standard Normal Distribution
2.2
Regression
2.2.1
RMS Error of Fit
2.2.2
The Regression Line
2.2.3
The Scatter Diagram
2.2.4
More on Prediction and Error
2.2.5
Facts about the correlation coefficient
\(r\)
2.2.6
The Regression Effect and the Regression Fallacy
2.3
Probability
2.3.1
Box Models
2.3.2
Complement, Intersection, Union of Events
2.3.3
Conditional Probability
2.3.4
Independent and Dependent Events
2.3.5
Probability Rules
2.3.6
The Binomial Formula
2.4
Sampling Theory
2.4.1
Sampling Vocabulary and Formulas
2.4.2
The Central Limit Theorem
2.4.3
Basic prediction problem
2.4.4
Basic Inference Problem
Back Matter
Colophon
About the author
Index
Notation
References
A
In-Class Activities
A.1
Activity on Medical Testing
A.2
Batting Average Puzzle
A.3
Rectangle Area Puzzle
A.4
Intuition for Average and SD
A.5
Vocabulary Practice
A.5.1
Descriptive Statistics
A.5.2
Two-variable data
A.5.3
Probability
A.5.4
Sampling
Elementary Statistics Supplementary Notes
David W. Lyons
Department of Mathematical Sciences
Lebanon Valley College
Annville, PA, USA
lyons@lvc.edu
©2021 David W. Lyons
January 2025 Edition, revised: December 16, 2024
Preface
