Skip to Content
OpenStax Logo
Introductory Statistics

Index

Introductory StatisticsIndex
Buy book
  1. Preface
  2. 1 Sampling and Data
    1. Introduction
    2. 1.1 Definitions of Statistics, Probability, and Key Terms
    3. 1.2 Data, Sampling, and Variation in Data and Sampling
    4. 1.3 Frequency, Frequency Tables, and Levels of Measurement
    5. 1.4 Experimental Design and Ethics
    6. 1.5 Data Collection Experiment
    7. 1.6 Sampling Experiment
    8. Key Terms
    9. Chapter Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  3. 2 Descriptive Statistics
    1. Introduction
    2. 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
    3. 2.2 Histograms, Frequency Polygons, and Time Series Graphs
    4. 2.3 Measures of the Location of the Data
    5. 2.4 Box Plots
    6. 2.5 Measures of the Center of the Data
    7. 2.6 Skewness and the Mean, Median, and Mode
    8. 2.7 Measures of the Spread of the Data
    9. 2.8 Descriptive Statistics
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  4. 3 Probability Topics
    1. Introduction
    2. 3.1 Terminology
    3. 3.2 Independent and Mutually Exclusive Events
    4. 3.3 Two Basic Rules of Probability
    5. 3.4 Contingency Tables
    6. 3.5 Tree and Venn Diagrams
    7. 3.6 Probability Topics
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Bringing It Together: Practice
    13. Homework
    14. Bringing It Together: Homework
    15. References
    16. Solutions
  5. 4 Discrete Random Variables
    1. Introduction
    2. 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
    3. 4.2 Mean or Expected Value and Standard Deviation
    4. 4.3 Binomial Distribution
    5. 4.4 Geometric Distribution
    6. 4.5 Hypergeometric Distribution
    7. 4.6 Poisson Distribution
    8. 4.7 Discrete Distribution (Playing Card Experiment)
    9. 4.8 Discrete Distribution (Lucky Dice Experiment)
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. References
    16. Solutions
  6. 5 Continuous Random Variables
    1. Introduction
    2. 5.1 Continuous Probability Functions
    3. 5.2 The Uniform Distribution
    4. 5.3 The Exponential Distribution
    5. 5.4 Continuous Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  7. 6 The Normal Distribution
    1. Introduction
    2. 6.1 The Standard Normal Distribution
    3. 6.2 Using the Normal Distribution
    4. 6.3 Normal Distribution (Lap Times)
    5. 6.4 Normal Distribution (Pinkie Length)
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  8. 7 The Central Limit Theorem
    1. Introduction
    2. 7.1 The Central Limit Theorem for Sample Means (Averages)
    3. 7.2 The Central Limit Theorem for Sums
    4. 7.3 Using the Central Limit Theorem
    5. 7.4 Central Limit Theorem (Pocket Change)
    6. 7.5 Central Limit Theorem (Cookie Recipes)
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  9. 8 Confidence Intervals
    1. Introduction
    2. 8.1 A Single Population Mean using the Normal Distribution
    3. 8.2 A Single Population Mean using the Student t Distribution
    4. 8.3 A Population Proportion
    5. 8.4 Confidence Interval (Home Costs)
    6. 8.5 Confidence Interval (Place of Birth)
    7. 8.6 Confidence Interval (Women's Heights)
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. Solutions
  10. 9 Hypothesis Testing with One Sample
    1. Introduction
    2. 9.1 Null and Alternative Hypotheses
    3. 9.2 Outcomes and the Type I and Type II Errors
    4. 9.3 Distribution Needed for Hypothesis Testing
    5. 9.4 Rare Events, the Sample, Decision and Conclusion
    6. 9.5 Additional Information and Full Hypothesis Test Examples
    7. 9.6 Hypothesis Testing of a Single Mean and Single Proportion
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. Solutions
  11. 10 Hypothesis Testing with Two Samples
    1. Introduction
    2. 10.1 Two Population Means with Unknown Standard Deviations
    3. 10.2 Two Population Means with Known Standard Deviations
    4. 10.3 Comparing Two Independent Population Proportions
    5. 10.4 Matched or Paired Samples
    6. 10.5 Hypothesis Testing for Two Means and Two Proportions
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  12. 11 The Chi-Square Distribution
    1. Introduction
    2. 11.1 Facts About the Chi-Square Distribution
    3. 11.2 Goodness-of-Fit Test
    4. 11.3 Test of Independence
    5. 11.4 Test for Homogeneity
    6. 11.5 Comparison of the Chi-Square Tests
    7. 11.6 Test of a Single Variance
    8. 11.7 Lab 1: Chi-Square Goodness-of-Fit
    9. 11.8 Lab 2: Chi-Square Test of Independence
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  13. 12 Linear Regression and Correlation
    1. Introduction
    2. 12.1 Linear Equations
    3. 12.2 Scatter Plots
    4. 12.3 The Regression Equation
    5. 12.4 Testing the Significance of the Correlation Coefficient
    6. 12.5 Prediction
    7. 12.6 Outliers
    8. 12.7 Regression (Distance from School)
    9. 12.8 Regression (Textbook Cost)
    10. 12.9 Regression (Fuel Efficiency)
    11. Key Terms
    12. Chapter Review
    13. Formula Review
    14. Practice
    15. Homework
    16. Bringing It Together: Homework
    17. References
    18. Solutions
  14. 13 F Distribution and One-Way ANOVA
    1. Introduction
    2. 13.1 One-Way ANOVA
    3. 13.2 The F Distribution and the F-Ratio
    4. 13.3 Facts About the F Distribution
    5. 13.4 Test of Two Variances
    6. 13.5 Lab: One-Way ANOVA
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  15. A | Review Exercises (Ch 3-13)
  16. B | Practice Tests (1-4) and Final Exams
  17. C | Data Sets
  18. D | Group and Partner Projects
  19. E | Solution Sheets
  20. F | Mathematical Phrases, Symbols, and Formulas
  21. G | Notes for the TI-83, 83+, 84, 84+ Calculators
  22. H | Tables
  23. Index
Symbols
α9.4 Rare Events, the Sample, Decision and Conclusion
A
absolute value of a residual12.3 The Regression Equation
alternative hypothesis9.1 Null and Alternative Hypotheses
Area to the left 6.2 Using the Normal Distribution
Area to the right 6.2 Using the Normal Distribution
assumption9.4 Rare Events, the Sample, Decision and Conclusion
average1.1 Definitions of Statistics, Probability, and Key Terms
B
balanced design13.3 Facts About the F Distribution
bar graph1.2 Data, Sampling, and Variation in Data and Sampling
Bernoulli Trial4.3 Binomial Distribution
binomial distribution7.3 Using the Central Limit Theorem, 8.3 A Population Proportion, 9.3 Distribution Needed for Hypothesis Testing
binomial probability distribution4.3 Binomial Distribution
bivariateIntroduction
Blinding1.4 Experimental Design and Ethics
Box plots2.4 Box Plots
box-and-whisker plots2.4 Box Plots
box-whisker plots2.4 Box Plots
C
categorical data1.2 Data, Sampling, and Variation in Data and Sampling
Categorical variables1.1 Definitions of Statistics, Probability, and Key Terms
central limit theoremIntroduction, 7.1 The Central Limit Theorem for Sample Means (Averages), 7.3 Using the Central Limit Theorem, 9.5 Additional Information and Full Hypothesis Test Examples
central limit theorem for means7.1 The Central Limit Theorem for Sample Means (Averages)
central limit theorem for sums7.2 The Central Limit Theorem for Sums
chi-square distribution11.1 Facts About the Chi-Square Distribution
coefficient of determination12.3 The Regression Equation
Cohen's d10.1 Two Population Means with Unknown Standard Deviations
complement3.1 Terminology
conditional probability3.1 Terminology, 5.2 The Uniform Distribution
confidence intervalIntroduction, 8.2 A Single Population Mean using the Student t Distribution
confidence intervals8.3 A Population Proportion, Introduction
confidence level8.1 A Single Population Mean using the Normal Distribution, 8.3 A Population Proportion
contingency table3.4 Contingency Tables, 11.3 Test of Independence
continuity correction factor7.3 Using the Central Limit Theorem
continuous1.2 Data, Sampling, and Variation in Data and Sampling
continuous random variable5.3 The Exponential Distribution
control group1.4 Experimental Design and Ethics
critical value6.2 Using the Normal Distribution
cumulative distribution function (CDF)5.3 The Exponential Distribution
Cumulative relative frequency1.3 Frequency, Frequency Tables, and Levels of Measurement
D
data1.1 Definitions of Statistics, Probability, and Key Terms, 1.1 Definitions of Statistics, Probability, and Key Terms
degrees of freedom8.2 A Single Population Mean using the Student t Distribution
degrees of freedom (df)10.1 Two Population Means with Unknown Standard Deviations
descriptive statistics1.1 Definitions of Statistics, Probability, and Key Terms
discrete1.2 Data, Sampling, and Variation in Data and Sampling
double-blind experiment1.4 Experimental Design and Ethics
E
Empirical Rule6.1 The Standard Normal Distribution, Introduction
equal standard deviations13.1 One-Way ANOVA
Equally likely3.1 Terminology, 5.2 The Uniform Distribution
error bound8.3 A Population Proportion
error bound for a population mean8.1 A Single Population Mean using the Normal Distribution, 8.2 A Single Population Mean using the Student t Distribution
event3.1 Terminology
expected value4.2 Mean or Expected Value and Standard Deviation, 4.2 Mean or Expected Value and Standard Deviation
expected values11.2 Goodness-of-Fit Test
experiment3.1 Terminology
experimental unit1.4 Experimental Design and Ethics
explanatory variable1.4 Experimental Design and Ethics
exponential distribution5.3 The Exponential Distribution, 7.3 Using the Central Limit Theorem
extrapolation12.5 Prediction
F
F distribution13.2 The F Distribution and the F-Ratio
F ratio13.2 The F Distribution and the F-Ratio
fair3.1 Terminology
first quartile2.3 Measures of the Location of the Data
frequency1.3 Frequency, Frequency Tables, and Levels of Measurement, 2.2 Histograms, Frequency Polygons, and Time Series Graphs
G
geometric distribution4.4 Geometric Distribution
goodness-of-fit test11.2 Goodness-of-Fit Test
H
histogram2.2 Histograms, Frequency Polygons, and Time Series Graphs
hypergeometric experiment4.8 Discrete Distribution (Lucky Dice Experiment)
hypergeometric probability4.5 Hypergeometric Distribution
hypotheses9.1 Null and Alternative Hypotheses
hypothesis test9.3 Distribution Needed for Hypothesis Testing, 9.5 Additional Information and Full Hypothesis Test Examples, 9.6 Hypothesis Testing of a Single Mean and Single Proportion
hypothesis testingIntroduction
I
independent3.2 Independent and Mutually Exclusive Events, 3.3 Two Basic Rules of Probability
Independent groupsIntroduction
inferential statistics1.1 Definitions of Statistics, Probability, and Key Terms, Introduction
influential points12.6 Outliers
informed consent1.4 Experimental Design and Ethics
Institutional Review Boards (IRB)1.4 Experimental Design and Ethics
interpolation12.5 Prediction
interquartile range2.3 Measures of the Location of the Data
interval scale1.3 Frequency, Frequency Tables, and Levels of Measurement
L
law of large numbers3.1 Terminology, 7.3 Using the Central Limit Theorem
Least-Squares Line12.3 The Regression Equation
least-squares regression line12.3 The Regression Equation
level of measurement1.3 Frequency, Frequency Tables, and Levels of Measurement
Line of Best Fit12.3 The Regression Equation
linear regression12.2 Scatter Plots
long-term relative frequency3.1 Terminology
lurking variables1.4 Experimental Design and Ethics
M
margin of errorIntroduction
matched pairsIntroduction
mean1.1 Definitions of Statistics, Probability, and Key Terms, 1.1 Definitions of Statistics, Probability, and Key Terms, 2.5 Measures of the Center of the Data, 4.2 Mean or Expected Value and Standard Deviation, Introduction, 7.1 The Central Limit Theorem for Sample Means (Averages), 7.3 Using the Central Limit Theorem
mean square13.2 The F Distribution and the F-Ratio
median2.3 Measures of the Location of the Data, 2.5 Measures of the Center of the Data
mode2.5 Measures of the Center of the Data
multivariateIntroduction
mutually exclusive3.2 Independent and Mutually Exclusive Events, 3.3 Two Basic Rules of Probability
N
nominal scale1.3 Frequency, Frequency Tables, and Levels of Measurement
normal approximation to the binomial7.3 Using the Central Limit Theorem
normal distribution8.2 A Single Population Mean using the Student t Distribution, 8.3 A Population Proportion, 9.3 Distribution Needed for Hypothesis Testing, 10.2 Two Population Means with Known Standard Deviations
normally distributed7.1 The Central Limit Theorem for Sample Means (Averages), 7.2 The Central Limit Theorem for Sums, 9.3 Distribution Needed for Hypothesis Testing
null hypothesis9.1 Null and Alternative Hypotheses, 9.4 Rare Events, the Sample, Decision and Conclusion, 9.4 Rare Events, the Sample, Decision and Conclusion, 9.4 Rare Events, the Sample, Decision and Conclusion
Numerical variables1.1 Definitions of Statistics, Probability, and Key Terms
O
observed values11.2 Goodness-of-Fit Test
ordinal scale1.3 Frequency, Frequency Tables, and Levels of Measurement
outcome3.1 Terminology
outlier2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs, 2.3 Measures of the Location of the Data
outliers12.6 Outliers
P
p-value9.4 Rare Events, the Sample, Decision and Conclusion, 9.5 Additional Information and Full Hypothesis Test Examples
paired data set2.2 Histograms, Frequency Polygons, and Time Series Graphs
parameter1.1 Definitions of Statistics, Probability, and Key Terms, Introduction
Pareto chart1.2 Data, Sampling, and Variation in Data and Sampling
Pearson1.1 Definitions of Statistics, Probability, and Key Terms
percentile7.2 The Central Limit Theorem for Sums
percentiles2.3 Measures of the Location of the Data
pie chart1.2 Data, Sampling, and Variation in Data and Sampling
placebo1.4 Experimental Design and Ethics
point estimateIntroduction
Poisson probability distribution4.6 Poisson Distribution, 4.8 Discrete Distribution (Lucky Dice Experiment)
population1.1 Definitions of Statistics, Probability, and Key Terms, 1.2 Data, Sampling, and Variation in Data and Sampling
population variance11.6 Test of a Single Variance
potential outlier12.6 Outliers
Probability1.1 Definitions of Statistics, Probability, and Key Terms, 3.1 Terminology
probability density functionIntroduction
probability distribution function4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
proportion1.1 Definitions of Statistics, Probability, and Key Terms
Q
Qualitative data1.2 Data, Sampling, and Variation in Data and Sampling
quantitative continuous data1.2 Data, Sampling, and Variation in Data and Sampling
Quantitative data1.2 Data, Sampling, and Variation in Data and Sampling
quantitative discrete data1.2 Data, Sampling, and Variation in Data and Sampling
quartiles2.3 Measures of the Location of the Data, 2.3 Measures of the Location of the Data
R
random assignment1.4 Experimental Design and Ethics
random variableIntroduction, 10.1 Two Population Means with Unknown Standard Deviations, 10.2 Two Population Means with Known Standard Deviations
ratio scale1.3 Frequency, Frequency Tables, and Levels of Measurement
relative frequency1.3 Frequency, Frequency Tables, and Levels of Measurement, 2.2 Histograms, Frequency Polygons, and Time Series Graphs
replacement3.2 Independent and Mutually Exclusive Events
representative sample1.1 Definitions of Statistics, Probability, and Key Terms
residual12.3 The Regression Equation
response variable1.4 Experimental Design and Ethics
S
sample1.1 Definitions of Statistics, Probability, and Key Terms
sample mean7.1 The Central Limit Theorem for Sample Means (Averages)
sample size7.1 The Central Limit Theorem for Sample Means (Averages), 7.2 The Central Limit Theorem for Sums
sample space3.1 Terminology, 3.3 Two Basic Rules of Probability, 3.5 Tree and Venn Diagrams
samples1.2 Data, Sampling, and Variation in Data and Sampling
sampling1.1 Definitions of Statistics, Probability, and Key Terms
sampling distribution2.5 Measures of the Center of the Data
sampling variability of a statistic2.7 Measures of the Spread of the Data
simple random sample9.3 Distribution Needed for Hypothesis Testing
single population mean9.3 Distribution Needed for Hypothesis Testing
single population proportion9.3 Distribution Needed for Hypothesis Testing
standard deviation2.7 Measures of the Spread of the Data, 8.2 A Single Population Mean using the Student t Distribution, 9.3 Distribution Needed for Hypothesis Testing, 9.3 Distribution Needed for Hypothesis Testing, 9.4 Rare Events, the Sample, Decision and Conclusion, 9.5 Additional Information and Full Hypothesis Test Examples
standard error10.1 Two Population Means with Unknown Standard Deviations
standard error of the mean.7.1 The Central Limit Theorem for Sample Means (Averages)
standard normal distribution6.1 The Standard Normal Distribution
statistic1.1 Definitions of Statistics, Probability, and Key Terms
statistics1.1 Definitions of Statistics, Probability, and Key Terms
Student's t-distribution8.2 A Single Population Mean using the Student t Distribution, 9.3 Distribution Needed for Hypothesis Testing, 9.3 Distribution Needed for Hypothesis Testing
Sum of Squared Errors (SSE)12.3 The Regression Equation
sum of squares13.2 The F Distribution and the F-Ratio
T
test for homogeneity11.4 Test for Homogeneity
test of a single variance11.6 Test of a Single Variance
test of independence11.3 Test of Independence
test statistic10.2 Two Population Means with Known Standard Deviations
The standard deviation10.2 Two Population Means with Known Standard Deviations
third quartile2.3 Measures of the Location of the Data
treatments1.4 Experimental Design and Ethics
tree diagram3.5 Tree and Venn Diagrams
Type I error9.2 Outcomes and the Type I and Type II Errors, 9.4 Rare Events, the Sample, Decision and Conclusion
Type II error9.2 Outcomes and the Type I and Type II Errors
U
unfair3.1 Terminology
uniform distribution7.3 Using the Central Limit Theorem
V
variable1.1 Definitions of Statistics, Probability, and Key Terms
variance2.7 Measures of the Spread of the Data
Variance between samples13.2 The F Distribution and the F-Ratio
Variance within samples13.2 The F Distribution and the F-Ratio
variances13.1 One-Way ANOVA
Variation1.2 Data, Sampling, and Variation in Data and Sampling
Venn diagram3.5 Tree and Venn Diagrams
Z
z-score8.2 A Single Population Mean using the Student t Distribution
z-scores6.1 The Standard Normal Distribution
Previous
Citation/Attribution

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
Citation information

© Jan 22, 2020 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 license. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.