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    COURSE INTRODUCTION
    Course Syllabus
    Unit 1: Statistics and Data
    1.1.1: What is Statistics?
    What are Statistics?
    1.1.2: Descriptive and Inferential Statistics
    Descriptive and Inferential Statistics
    Basic Definitions and Concepts
    1.1.3: Types of Data and Their Collection
    Variables and Data Collection
    Presenting Data
    1.2.1: Graphical Methods for Describing Quantitative Data
    Graphing
    Three Popular Data Displays
    1.2.2: Numerical Measures of Central Tendency and Variability
    Numerical Measures of Central Tendency and Variability
    Measures of Central Location
    Mean, Median, Mode, and Variance
    1.2.3: Methods for Describing Relative Standing
    Percentiles
    1.2.4: Methods for Describing Bivariate Relationships
    Scatterplots and Bivariate Data
    Pearson's r
    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Elements of Probability and Random Variables
    2.1.1: Events, Sample Spaces, and Probability
    Introduction to Probability
    Basic Concepts of Probability
    2.1.2: Counting Rules
    Permutations and Combinations
    The Addition Rule for Probability with a Venn Diagram Example
    2.2.1: Common Discrete Random Variables
    Random Variables and Probability Distributions
    Binomial Distributions
    Binomial, Poisson, and Multinomial Distributions
    2.2.2: Normal Distribution
    The Standard Normal Distribution
    More on Normal Distributions
    Introduction to the Normal Distribution
    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: Sampling Distributions
    3.1.1: Continuous Random Variables
    Continuous Random Variables
    3.1.2: Definition and Interpretation
    Introduction to Sampling Distributions
    3.1.3: Sampling Distributions Properties
    Wolfram Demonstrations Project
    3.2.1: The Sampling Distribution of Sample Mean
    The Sampling Distribution of a Sample Mean
    The Mean, Standard Deviation, and Sampling Distribution of the Sample Mean
    Sampling Distribution
    3.2.2: The Sampling Distribution of Pearson's r
    Sampling Distribution of r
    3.2.3: The Sampling Distribution of the Sample Proportion
    Sampling Distribution of p
    Standard Deviation
    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Estimation with Confidence Intervals
    4.1.1: Sample Statistics and Parameters
    Basic Sample Statistics and Parameters
    4.1.2: Bias and Sampling Variability
    Characteristics of Estimators
    4.2.1: Confidence Intervals for Mean
    Confidence Intervals for the Mean
    Demonstration: Confidence Intervals for a Mean
    t Distribution Demonstration
    Comparing Normal and Student's t-Distributions
    4.2.2: Confidence Intervals for Correlation and Proportion
    Confidence Intervals for Correlation and Proportion
    Confidence Intervals
    Unit 4 Assessment
    Unit 4 Assessment
    Unit 5: Hypothesis Test
    5.1.1: Setting up Hypotheses
    Setting Up Hypotheses
    5.1.2: Interpreting Hypotheses Testing Results
    The Observed Significance of a Test
    Results
    Hypothesis Testing with One Sample
    More on Hypothesis Testing
    5.1.3: Steps in Hypothesis Testing and Its Relation to Confidence Intervals
    Steps and Confidence Intervals in Hypothesis Testing
    5.2.1: Testing Single Mean
    Testing a Single Mean
    Sample Tests for a Population Mean
    5.2.2: Testing the Difference between Two Means
    The Difference between Two Means
    Difference of Means
    5.3: Chi-Square Distribution
    Contingency Tables
    Chi-Square Distributions and Goodness of Fit
    More on Chi-square Distributions
    5.4: Comparing the Proportions of Populations
    Comparing Population Proportions
    Unit 5 Assessment
    Unit 5 Assessment
    Unit 6: Linear Regression
    6.1.1: Scatter Plot of Two Variables and Regression Line
    Introduction to Linear Regression
    Linear Regression
    6.1.2: Correlation Coefficient
    Correlation
    The Linear Correlation Coefficient
    6.1.3: Sums of Squares
    Partitioning Sums of Squares
    Regression Lines
    6.2.1: Standard Errors of the Least Squares Estimates
    Standard Error of the Estimate
    6.2.2: Statistical Inference for the Slope and Correlation
    Inferential Statistics for b and r
    Statistical Inference about Slope
    6.2.3: Influential Observations
    Influential Observations
    A Complete Example
    6.3: ANOVA
    ANOVA
    More on ANOVA
    Unit 6 Assessment
    Unit 6 Assessment
    Study Guide
    MA121 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    MA121: Certificate Final Exam
    Archived Materials
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Table of contents

  • Introduction
    • Video
    • Questions
    • Answers
  1. MA121: Introduction to Statistics
  2. Unit 2: Elements of Probability and Random Variables
  3. 2.1: Classical Probability Model
  4. 2.1.2: Counting Rules
  5. Permutations and Combinations

Permutations and Combinations

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This section introduces formulas for combinations and permutations, which are helpful in computing probabilities.

 

https://onlinestatbook.com/movies/probability/permutations.mp4
 

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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.