Back to Learning Catalog

Open

36 Weeks

### Overview

Probability and Statistics will introduce students to exploring data, sampling and experimentation by planning and conducting studies, anticipating patterns using probability and simulation, and employing statistical inference to analyze data and draw conclusions.

### Course Requirements

Required Materials:

• Graphing Calculator

### Major Topics and Concepts

Segment I Concepts

Module 01: Exploring DataIntroduction to Statistics

• Measures of Central Tendency
• Measures of Variation
• Displaying Data

Module 02: Collecting Data

• Sampling and Surveys
• Experiments
• Correlation Versus Causation

Module 03: Probability

• Basic Concepts of Probability
• Condition Probability and Two-Way Tables
• The Multiplication and Addition Rule
• Simulations

Segment II Concepts

Module 04: Probability Distributions

• Random Variables
• Binomial Probability Distribution
• Geometric Probability Distribution
• Introduction to Normal Probability Distribution

Module 05: Sampling Distribution

• Sampling Distributions and Proportions
• Sample Means
• Confidence Intervals for Proportions
• Confidence Intervals for Means

Module 06: Inference

• Hypothesis Testing- One Proportion
• Hypothesis Testing- One-Sample Mean
• Comparing Two Means
• Scatterplots and Correlation
• Least-Squares Regression

### Competencies

• Introduction to Statistics
Students will demonstrate an understanding of statistical concepts by examining data types, using measures of central tendency and variation, and interpreting graphs for items such as categorical trends, statistical evaluations, and quantitative measurements.
• Surveys and Sample Sets
Students will demonstrate an understanding of surveys and sample sets by evaluating sampling methods, sampling bias, and sampling errors.
• Experimental and Observational Studies
Students will demonstrate an understanding of experimental and observational studies by evaluating the relationship between variables, designing an experiment or an observational study to investigate variables, and analyzing the statistical data generated by the investigation of the variables.
• Rules of Probability
Students will demonstrate an understanding of the rules of probability by applying the rules of probability to solve problems, evaluating independent and mutually exclusive events, and performing statistical evaluations of probability data.
• Simulations
Students will demonstrate an understanding of simulated data collection by completing a simulation where they identifying a problem, evaluating the assumptions, analyzing the process, and summarizing the conclusions.
• Binomial, Geometric and Normal Probability Distributions
Students will demonstrate an understanding of binomial distributions, geometric distributions, and normal distributions by identifying the characteristics of each type of distribution and performing statistical operations such as characterizing random variables, identifying conditions to evaluate random variables, and standardizing the distribution of those variables.
• Sampling Distributions, Proportions, and Means
Students will demonstrate an understanding of sampling distributions, proportions, and means by characterizing sampling and population distributions, performing statistical evaluations of sampling distribution data, evaluating x-bar graphs, and analyzing the Central Limit Theorem.
• Confidence Intervals
Students will demonstrate an understanding of confidence intervals by characterizing a confidence interval, evaluating random, normal and independent conditions, performing statistical evaluations on the intervals, and constructing confidence intervals for means within a group.
• Hypothesis Testing
Students will demonstrate an understanding of hypothesis testing for both means and proportions for one and two populations by the evaluation of a classical hypothesis test, analyzing statistical distribution data, constructing confidence intervals, and performing hypothesis tests
• Bivariate Data
Students will demonstrate an understanding of the relationships for bivariate data by evaluating scatterplots, performing statistical analysis on linear relationships, interpreting computer regression output of least-squares regression line (LSRL), and determining association or causation using LSRL.

Algebra 1

## Attend a virtual open house

We offer regular online open house webinars where VLACS staff members provide parents and students with an overview of our programs and answer questions about online learning.