# Ch 22: Working with Data & Statistics

### About This Chapter

## Working with Data & Statistics - Chapter Summary

Use this chapter to practice making estimates and predictions with both categorical and quantitative data. Video lessons cover the following topics to prepare you for these types of data analysis and statistics questions on the SAT level 2 mathematics subject test:

- Bar graphs, pie charts and histograms
- Relative and cumulative frequency tables
- Measures of central tendency
- Standard deviation and shifts in the mean
- Quartiles and the interquartile range
- Line graphs and simple linear regression
- Quadratic and exponential regression

In addition to videos containing plenty of sample charts, graphs and tables, lessons in this chapter are accompanied by transcripts that allow you to view the material at a glance. If you'd like to try your hand at working with data and statistics, this chapter also includes several self-assessment quizzes you can use to determine how much more study time you need to put in and familiarize yourself with test question formatting.

### Working with Data & Statistics - Chapter Objectives

If you completed trigonometry or precalculus courses as part of your high school curriculum, you might consider submitting scores on the SAT level 2 mathematics subject test to demonstrate your interest in this area to college admission departments. Some schools might also use your scores to place you in intermediate-level math courses or require them as part of the admissions process.

Around 10% of SAT level 2 mathematics test questions cover the area of data analysis, statistics and probability. It's on this part of the exam where a familiarity with mean, median, mode, standard deviation, linear regression and other topics covered in this chapter will come in handy. Additional test questions cover the areas of geometry, algebra and number operations. There are 50 multiple-choice questions altogether, and you'll be given an hour to complete them.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. What is a Two-Way Table?

Do you believe in Martians? Do you watch football on television? A Two-Way Table or Contingency Table is a great way to show the results of all kinds of survey questions. In this video we will learn how to read a two-way table.

### 6. 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.

### 7. 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.

### 8. What is a Histogram in Math? - Definition & Examples

Watch this video lesson to see how useful a histogram can be when you need to show a bunch of data in an easy to read format. Also, learn how you can easily gather the information you need from looking at a histogram.

### 9. What are Center, Shape, and Spread?

Center, shape, and spread are all words that describe what a particular graph looks like. Watch this video lesson to see how you can identify and explain each.

### 10. 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.

### 11. Describing the Relationship between Two Quantitative Variables

In this video lesson, you will learn about quantitative variables, what they are, and how one variable relates to another. You will learn why this is important and why it can sometimes even save lives.

### 12. 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.

### 13. Quartiles & the Interquartile Range: Definition, Formulate & Examples

Quartiles and the interquartile range can be used to group and analyze data sets. In this lesson, learn the definition and steps for finding the quartiles and interquartile range for a given data set.

### 14. 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.

### 15. 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.

### 16. Simple Linear Regression: Definition, Formula & Examples

Simple linear regression is a great way to make observations and interpret data. In this lesson, you will learn to find the regression line of a set of data using a ruler and a graphing calculator.

### 17. Problem Solving Using Linear Regression: Steps & Examples

Linear regression can be a powerful tool for predicting and interpreting information. Learn to use two common formulas for linear regression in this lesson.

### 18. Least-Squares Regression: Definition, Equations & Examples

In this lesson, we will explore least-squares regression and show how this method relates to fitting an equation to some data. Using examples, we will learn how to predict a future value using the least-squares regression method.

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### Other Chapters

Other chapters within the SAT Subject Test Mathematics Level 2: Practice and Study Guide course

- Structure & Strategies for the SAT Math Level 2
- Basic Math Review
- Square Roots
- Basic Algebraic Expressions
- Exponents
- Vectors
- Algebraic Linear Equations & Inequalities
- Algebra: Absolute Value Equations & Inequalities
- Algebra: Polynomials
- Functions in Math
- Algebra: Rational Expressions
- Matrices
- Understanding Sequences & Series
- Understanding Exponentials & Logarithms
- Complex and Imaginary Numbers
- Coordinate Geometry Basics
- Coordinate Geometry: Graphing Linear Equations & Inequalities
- Advanced Coordinate Geometry
- Three-Dimensional Geometry
- Overview of Trigonometry
- Probability, Combinations & Permutations
- Basic Mathematical Logic
- Limits of Functions
- SAT Subject Test Mathematics Level 2 Flashcards