MTH413: Probability and Statistics (Comprehensive)

This list is representative of the materials provided or used in this course. Keep in mind that the actual materials used may vary, depending on the school in which you are enrolled, and whether you are taking the course as Independent Study.

For a complete list of the materials to be used in this course by your enrolled student, please visit MyInfo. All lists are subject to change at any time.

Scope & Sequence : Scope & Sequence documents describe what is covered in a course (the scope) and also the order in which topics are covered (the sequence). These documents list instructional objectives and skills to be mastered. K12 Scope & Sequence documents for each course include:

Course Overview

Students learn counting methods, probability, descriptive statistics, graphs of data, the normal curve, statistical inference, and linear regression. Proficiency is measured through frequent online and offline assessments, as well as asynchronous discussions. Problem-solving activities provide an opportunity for students to demonstrate their skills in real-world situations.

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Course Length

One Semester

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Three years of high school mathematics.

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Course Outline

Unit 1: Representing Data Graphically

Students develop skills and instincts that will allow them to create clear, convincing presentations of any data set they encounter. They also learn to look at any data chart or plot with a critical, mathematical eye and point out trends and important features of the data. They work on an extended graphing exercise throughout the unit and prepare a presentation. Topics include:

  • Course Introduction
  • Introduction: Representing Data Graphically
  • Data and Variables
  • Graphs of Categorical Data
  • Two-Way Tables
  • Line Plots
  • Frequency Tables
  • Histograms
  • Stem-and-Leaf Plots
  • Time Series Plots

Unit 2: Representing Data Numerically

Students work with real data from 55 national parks in the United States, learning how to represent an entire set of data by using single numbers that describe where the center of the distribution is located and how the data are spread. Topics include:

  • Introduction: Representing Data Numerically
  • Measures of Center
  • Box Plots
  • Determining Quartiles
  • Outliers
  • Comparing Data Sets 
  • Measuring Spread
  • Transforming Data Sets

Unit 3. Counting and Probability

Students learn mathematical formulas for counting large sets and determine the number of combinations and arrangements. They also learn basic probability and the difference between experimental and theoretical probability. Topics include:

  • Introduction: Counting and Probability
  • Counting Methods
  • Permutations
  • Combinations
  • Basic Probability
  • Geometric Probability
  • Mutually Exclusive Events
  • Overlapping Events
  • Independent and Dependent Events
  • Experimental Probability

Unit 4. Random Variables and Distributions

Students begin to develop a more keen understanding of descriptive statistics. Topics include:

  • Introduction: Random Variables and Distributions
  • Creating Probability Distributions
  • Interpreting Probability Distributions
  • Expected Value
  • Binomial Distributions
  • Continuous Random Variables
  • The Normal Distribution
  • Standardizing Data
  • Comparing Scores
  • The Standard Normal Curve
  • Finding Standard Scores

Unit 5. Sampling

Students begin to learn about sampling and how to apply statistical methods to valid samples. Topics include:

  • Introduction: Sampling
  • Sample and Population
  • Bias in Sampling
  • Reducing Bias
  • Statistics and Parameters
  • Interval Estimates

Unit 6. Statistical Inference

Students learn how to put the power of statistics to work. Topics include:

  • Introduction: Statistical Inference
  • The Central Limit Theorem
  • Estimating Means
  • Mean Differences
  • Estimating Proportions
  • Proportion Differences

Unit 7. Relationships between Variables

Students learn how to identify and describe relationships between variables. Topics include:

  • Introduction: Relationships Between Variables
  • Scatter Plots
  • Association
  • The Correlation Coefficient
  • Fitting a Line to Data
  • Least Squares Regression
  • Regression Analysis
  • Cautions in Statistics

Unit 8: Semester Review and Test

Students review what they have learned and take the semester exam.

  • Semester Review
  • Semester Test
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Lesson Scheduling

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K12 Scope & Sequence documents for each course include:

  • Course Overview (as seen above)
  • Course Outline
  • Lesson Time and Scheduling