# Ch 25: Making Inferences & Justifying Conclusions in Math

### About This Chapter

## Making Inferences & Justifying Conclusions in Math - Chapter Summary

In statistics, it's important to have the ability to make inferences and justify conclusions. This chapter helps you sharpen these skills through bite-sized and entertaining lessons. Work through the chapter to review methods for interpreting expected values, comparing random variables, finding sample variance and much more. By the end of the chapter, you should be equipped to:

- Draw conclusions from sample surveys
- Differentiate between observational studies and experiments
- Assess the difference between statistics and parameters
- Explain the process of estimating sample data parameters
- Use equations for finding sample mean and variance
- Compare types of random variables
- Find/interpret the expected values of continuous random variables
- Develop continuous probability distributions

Each lesson comes with a short quiz that's designed to reinforce the information you study. Take these quizzes along with the chapter exam to master these mathematical concepts. You can watch the lessons online using your computer or mobile device, and you also have the option of printing our word-for-word lesson transcripts. Finally, if you have any questions, you can use the chapter's convenient Ask the Expert feature.

### 1. Drawing Conclusions from Sample Surveys

In this lesson, we look at a fictitious survey and show how to draw conclusions based on several criteria. Being able to discern the criteria of a good survey allows valid conclusions to follow the statistical analysis.

### 2. Experiments vs Observational Studies: Definition, Differences & Examples

There are different ways to collect data for research. In this lesson, you will learn about collecting data through observational studies and experiments and the differences between each.

### 3. Defining the Difference between Parameters & Statistics

Using data to describe information can be tricky. The first step is knowing the difference between populations and samples, and then parameters and statistics.

### 4. Estimating a Parameter from Sample Data: Process & Examples

One of the most useful things we can do with data is use it to describe a population. Learn how in this lesson as we discuss the concepts of parameters and samples.

### 5. Sample Mean & Variance: Definition, Equations & Examples

Sample mean and variance are both important statistics that can you can use to make predictions about a population. In this lesson, learn how to calculate these important values.

### 6. Random Variables: Definition, Types & Examples

This lesson defines the term random variables in the context of probability. You'll learn about certain properties of random variables and the different types of random variables.

### 7. Finding & Interpreting the Expected Value of a Continuous Random Variable

How can you find the expected value of something like height distributions? This lesson explains how to find and interpret the expected value of a continuous random variable.

### 8. Developing Continuous Probability Distributions Theoretically & Finding Expected Values

What is an expected value? How can you tell how many time you should expect a coin to land on heads out of several flips? This lesson will show you the answers to both questions!

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### Other Chapters

Other chapters within the TASC Mathematics: Prep and Practice course

- TASC Math: Real Numbers
- TASC Math: Complex and Imaginary Numbers Review
- Intro to Algebraic Expressions
- Intro to Algebraic Equations
- TASC Math: Exponents and Exponential Expressions
- Overview of Square Roots
- TASC Math: Radical Expressions
- TASC Math: Functions
- TASC Math: Graphing and Functions
- Overview of Sequences
- TASC Math: Inequalities
- TASC Math: Algebraic Distribution
- TASC Math: Linear Equations
- TASC Math: Factoring
- TASC Math: Quadratic Equations
- TASC Math: Graphing and Factoring Quadratic Equations
- TASC Math: Properties of Polynomial Functions
- TASC Math: Rational Expressions
- TASC Math: Measurement
- Lines, Angles & Arcs
- Shapes in Geometry
- Volume & Surface Area
- TASC Math: Calculations, Ratios, Percent & Proportions
- TASC Math: Data, Statistics, and Probability
- TASC Mathematics Flashcards