# Ch 19: Statistics, Probability & Working with Data

### About This Chapter

## Statistics, Probability & Working with Data - Chapter Summary

Lessons included in this chapter can show you how to use bar graphs, pie charts, scatter plots and tables to solve problems in the real world and correctly answer multiple-choice questions included on the math portion of the CAHSEE. You can also use the video lessons to review steps for calculating the following:

- Simple conditional probabilities
- Probability of simple, compound and complementary events
- Mean, median, mode and range
- Probability of independent and dependent events
- Statistical analyses and summaries of categorical data
- Probability of overlapping and non-overlapping events
- Estimates and predictions using quantitative data

These test preparation chapters include short, engaging video lessons and corresponding transcripts. These resources' video tags and lesson summaries allow you to review materials at your own pace and access key points quickly and easily. There are also self-assessment quizzes you can use to confirm your understanding of probability and statistics.

### Statistics, Probability & Working with Data - Objectives

The CAHSEE math section is designed to test your academic preparedness for a high school diploma in California. There are 80 multiple-choice questions in all, 12 of which are found in the exam's Statistics, Data Analysis and Probability section.

Questions covering this area ask you to interpret a graphical representation of data points or read a word problem before selecting the correct answer. You can use this chapter to brush up on vocabulary terms included on the test and review the uses of data to evaluate claims or express the probabilities of an event's possible outcomes.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. Understanding Bar Graphs and Pie Charts

In this lesson, we will examine two of the most widely used types of graphs: bar graphs and pie charts. These two graphs can provide the reader with a comparison of the different data that is displayed.

### 6. How to Calculate Mean, Median, Mode & Range

Measures of central tendency can provide valuable information about a set of data. In this lesson, explore how to calculate the mean, median, mode and range of any given data set.

### 7. How to Calculate Percent Increase with Relative & Cumulative Frequency Tables

In statistics, one way to describe and analyze data is by using frequency tables. This lesson will discuss relative and cumulative frequencies and how to calculate percent increase using these two methods.

### 8. 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.

### 9. Statistical Analysis with Categorical Data

Learn why percentages are so important when analyzing categorical data in this video lesson. Watch as the data is turned into a data table and a visual bar graph as ways to analyze the data.

### 10. Summarizing Categorical Data using Tables

Watch this video lesson to find out why data tables are an excellent way to summarize your categorical data. Learn what you need to do to your data before constructing a table and the two ways you can show your data.

### 11. Make Estimates and Predictions from Categorical Data

Categorical data can be estimated but not predicted. Learn why in this video lesson along with how to read and gather information from a bar graph of categorical data.

### 12. What is Quantitative Data? - Definition & Examples

Watch this video lesson to find out the difference between saying you have seven apples and saying that those apples are delicious. You will learn about quantitative data and why it is useful.

### 13. Reading and Interpreting Line Graphs

Watch this video lesson to find out how useful line graphs can be and how much information you can gain just from looking at one. Learn how you can apply that information in your own life to help you make better decisions.

### 14. Making Estimates and Predictions using Quantitative Data

Watch this video lesson to learn how you can read a scatter plot to learn more about a particular situation. Also learn how you can make estimates within the range of data you have and predict what may happen outside the range of data.

### 15. Creating & Interpreting Scatterplots: Process & Examples

Scatterplots are a great visual representation of two sets of data. In this lesson, you will learn how to interpret bivariate data to create scatterplots and understand the relationship between the two variables.

### 16. The Relationship Between Variables: Correlation Coefficient & Scatterplots

The focus of this lesson is on how both correlation coefficients and scatterplots convey the same message. Specifically, this lesson will explore how these two can reveal the same information but in different ways.

### 17. Statistics, Data Analysis & Probability in Real Life

In this lesson, we take a look at how statistics, data analysis, and probability can be incredibly useful in modern life. In fact, they very well may change your mind on everything from getting into college to winning the lottery.

### 18. Using Tables and Graphs in the Real World

We use tables and graphs in algebra as ways to visually show an equation or function. But do we really use these in the real world? Is it that important to learn about tables and graphs? Find out in this video lesson.

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### Other Chapters

Other chapters within the CAHSEE Math Exam: Test Prep & Study Guide course

- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Algebraic Linear Equations & Inequalities
- Problems with Exponents
- Overview of Functions
- Rational Expressions & Practice
- Calculations with Ratios, Percent & Proportions
- Understanding Matrices & Absolute Value
- Quadratics & Polynomials
- Geometry: Graphing Basics
- Graphing on the Coordinate Plane
- Measurement in Math
- Properties of Shapes
- Triangles, the Pythagorean Theorem & Congruency
- Perimeter, Area & Volume in Geometry
- Mathematical Reasoning
- Basic Mathematical Logic
- CAHSEE Math Exam Flashcards