# Ch 12: Praxis I Math: Basic Statistics and Probability

### About This Chapter

## Praxis I Math: Basic Statistics and Probability

This chapter is intended to help you learn about statistical variability, distributions, either/or probability, standard deviation and shifts in the mean. Other lesson topics you'll learn about related to basic statistics and probability include:

- Using random samplings to draw inferences about a population
- Investigating chance processes
- Evaluating and understanding random processes underlying statistical experiments
- Developing and using probability models
- Calculating simple conditional probabilities
- Probability of independent and dependent events
- Learning the 'At Least One' Rule
- Probability of simple, compound and complementary events
- Using probability to evaluate outcomes of decisions
- Understanding patterns of association in bi-variate data

Each lesson will be thoroughly explained by your video instructors as they show you how what you're learning can be used on the actual exam. The different learning approaches used throughout lessons are a way to keep them interesting and to ensure that you're ready for the exam.

### Objectives of the Basic Statistics and Probability Course

The chapter is designed to help you specifically with the data analysis and probability section of the Praxis, which is about 25% of the entire exam. You'll have a better idea of how to answer questions on the actual exam once you've completed this lesson's self-assessment quizzes in addition to seeing how much you've learned about basic statistics and probability.

The math test will measure the mathematical skills and ideas that an adult with a degree might need in addition to testing how well you can reason in a quantitative context and solve problems. There are about 12 multiple choice questions on the Praxis I Math test about data analysis and probability. You'll have 75 minutes to complete all 46 questions on the exam, but calculators are not allowed for the exam.

### 1. Measures of Variability: Range, Variance & Standard Deviation

Looking specifically at range, variance, and standard deviation, this lesson explores the relationship between these measures and samples, populations, and what it says about your data.

### 2. Normal Distribution: Definition, Properties, Characteristics & Example

In this lesson, we will look at the Normal Distribution, more commonly known as the Bell Curve. We'll look at some of its fascinating properties and learn why it is one of the most important distributions in the study of data.

### 3. Using the Normal Distribution: Practice Problems

In this lesson, we will put the normal distribution to work by solving a few practice problems that help us to really master all that the distribution, as well as Z-Scores, have to offer. Review the concepts with a short quiz at the end.

### 4. Calculating the Standard Deviation

In this lesson, we will examine the meaning and process of calculating the standard deviation of a data set. Standard deviation can help to determine if the data set is a normal distribution.

### 5. What is Random Sampling? - Definition, Conditions & Measures

Random sampling is used in many research scenarios. In this lesson, you will learn how to use random sampling and find out the benefits and risks of using random samples.

### 6. Simple Random Samples: Definition & Examples

Simple random sampling is a common method used to collect data in many different fields. From psychology to economics, simple random sampling can be the most feasible way to get information. Learn all about it in this lesson!

### 7. Dice: Finding Expected Values of Games of Chance

This lesson examines the various combinations and probabilities behind rolling dice. We will look at a game of dice and what to expect to win or lose in a game. In addition we will extend these concepts to playing with different sided dice.

### 8. Blackjack: Finding Expected Values of Games of Chance with Cards

In this video we learn about games of cards, and how to calculate probabilities. We look at the game of Blackjack and calculate the probability of getting certain hands. In addition we demonstrate how to calculate the expected value of a game that involves betting.

### 9. Lotteries: Finding Expected Values of Games of Chance

Most of us won't have a problem with winning the lottery. But is it a realistic goal? Do you really have a chance? In this lesson, learn how luck and probability collide when finding expected values in games of chance.

### 10. Random Selection & Random Allocation: Differences, Benefits & Examples

Random selection and random allocation are often confused with one another. This lesson will help you remember the differences between them and learn how to use each method.

### 11. How Randomized Experiments Are Designed

When reading research or when conducting your own, it is important to understand the basic concepts of randomized experimental design that are covered in this lesson.

### 12. Analyzing & Interpreting the Results of Randomized Experiments

Analyzing and interpreting the results of an experiment can be a confusing process, and it's easy to make mistakes. This lesson will help you understand the important factors of experiment analysis.

### 13. How to Calculate the Probability of Permutations

In this lesson, you will learn how to calculate the probability of a permutation by analyzing a real-world example in which the order of the events does matter. We'll also review what a factorial is. We will then go over some examples for practice.

### 14. How to Calculate the Probability of Combinations

To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.

### 15. How to Calculate a Permutation

A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.

### 16. How to Calculate Simple Conditional Probabilities

Conditional probability, just like it sounds, is a probability that happens on the condition of a previous event occurring. To calculate conditional probabilities, we must first consider the effects of the previous event on the current event.

### 17. Probability of Independent and Dependent Events

Sometimes probabilities need to be calculated when more than one event occurs. These types of compound events are called independent and dependent events. Through this lesson, we will look at some real-world examples of how to calculate these probabilities.

### 18. Probability of Independent Events: The 'At Least One' Rule

Occasionally when calculating independent events, it is only important that the event happens once. This is referred to as the 'At Least One' Rule. To calculate this type of problem, we will use the process of complementary events to find the probability of our event occurring at least once.

### 19. Probability of Simple, Compound and Complementary Events

Simple, compound, and complementary events are different types of probabilities. Each of these probabilities are calculated in a slightly different fashion. In this lesson, we will look at some real world examples of these different forms of probability.

### 20. Either/Or Probability: Overlapping and Non-Overlapping Events

Statistics is the study and interpretation of a set of data. One area of statistics is the study of probability. This lesson will describe how to determine the either/or probability of overlapping and non-overlapping events.

### 21. What is Bivariate Data? - Definition & Examples

In this lesson, you will be learning about the definition and uses of bivariate data. We will also compare and contrast the characteristics of univariate data and bivariate data.

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### Other Chapters

Other chapters within the Praxis Core Academic Skills for Educators - Mathematics (5732): Study Guide & Practice course

- About the Praxis Math Core Test
- Praxis I Math: The Real Number System
- Praxis I Math: Square Roots and Exponents
- Praxis I Math: Ratio and Proportions
- Praxis I Math: Algebraic Expressions
- Praxis I Math: Equations and Inequalities
- Praxis I Math: Functions
- Praxis I Math: Congruence and Similarity
- Praxis I Math: Right Triangles and Trigonometry
- Praxis I Math: Circles
- Praxis I Math: Geometric Measurement and Dimension
- Praxis I Math: Categorical and Quantitative Data
- Praxis Core Academic Skills for Educators: Math Flashcards