Math Review Large Print (18 point) Edition Chapter 4: Data ...

GRADUATE RECORD EXAMINATIONS?

Math Review Large Print (18 point) Edition

Chapter 4: Data Analysis

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The GRE? Math Review consists of 4 chapters: Arithmetic, Algebra, Geometry, and Data Analysis. This is the Large Print edition of the Data Analysis Chapter of the Math Review. Downloadable versions of large print (PDF) and accessible electronic format (Word) of each of the 4 chapters of the Math Review, as well as a Large Print Figure supplement for each chapter are available from the GRE? website. Other downloadable practice and test familiarization materials in large print and accessible electronic formats are also available. Tactile figure supplements for the 4 chapters of the Math Review, along with additional accessible practice and test familiarization materials in other formats, are available from ETS Disability Services, Monday to Friday 8:30 a.m. to 5 p.m. New York time, at 1-609-771-7780, or 1-866-387-8602 (toll free for test takers in the United States, U.S. Territories, and Canada), or via email at stassd@.

The mathematical content covered in this edition of the Math Review is the same as the content covered in the standard edition of the Math Review. However, there are differences in the presentation of some of the material. These differences are the result of adaptations made for presentation of the material in accessible formats. There are also slight differences between the various accessible formats, also as a result of specific adaptations made for each format.

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Table of Contents

Overview of the Math Review

4

Overview of this Chapter

5

4.1 Graphical Methods for Describing Data

6

4.2 Numerical Methods for Describing Data

28

4.3 Counting Methods

45

4.4 Probability

61

4.5 Distributions of Data, Random Variables, and

Probability Distributions

73

4.6 Data Interpretation Examples

104

Data Analysis Exercises

118

Answers to Data Analysis Exercises

132

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Overview of the Math Review

The Math Review consists of 4 chapters: Arithmetic, Algebra, Geometry, and Data Analysis.

Each of the 4 chapters in the Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and reason quantitatively on the Quantitative Reasoning measure of the GRE? revised General Test.

The material in the Math Review includes many definitions, properties, and examples, as well as a set of exercises (with answers) at the end of each chapter. Note, however, that this review is not intended to be all-inclusive--there may be some concepts on the test that are not explicitly presented in this review. If any topics in this review seem especially unfamiliar or are covered too briefly, we encourage you to consult appropriate mathematics texts for a more detailed treatment.

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Overview of this Chapter

This is the Data Analysis Chapter of the Math Review. The goal of data analysis is to understand data well enough to describe past and present trends, predict future events, and make good decisions. In this limited review of data analysis, we begin with tools for describing data; follow with tools for understanding counting and probability; review the concepts of distributions of data, random variables, and probability distributions; and end with examples of interpreting data.

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4.1 Graphical Methods for Describing Data

Data can be organized and summarized using a variety of methods. Tables are commonly used, and there are many graphical and numerical methods as well. The appropriate type of representation for a collection of data depends in part on the nature of the data, such as whether the data are numerical or nonnumerical. In this section, we review some common graphical methods for describing and summarizing data.

Variables play a major role in algebra because a variable serves as a convenient name for many values at once, and it also can represent a particular value in a given problem to solve. In data analysis, variables also play an important role but with a somewhat different meaning. In data analysis, a variable is any characteristic that can vary for the population of individuals or objects being analyzed. For example, both gender and age represent variables among people.

Data are collected from a population after observing either a single variable or observing more than one variable simultaneously. The distribution of a variable, or distribution of data, indicates the values of the variable and how frequently the values are observed in the data.

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Frequency Distributions

The frequency, or count, of a particular category or numerical value is the number of times that the category or value appears in the data. A frequency distribution is a table or graph that presents the categories or numerical values along with their associated frequencies. The relative frequency of a category or a numerical value is the associated frequency divided by the total number of data. Relative frequencies may be expressed in terms of percents, fractions, or decimals. A relative frequency distribution is a table or graph that presents the relative frequencies of the categories or numerical values.

Example 4.1.1: A survey was taken to find the number of children in each of 25 families. A list of the 25 values collected in the survey follows.

1 2 0 4 1 3 3 1 2 0 4 5 2 3 2 3 2 4 1 2 3 0 2 3 1

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The resulting frequency distribution of the number of children is presented in a 2-column table in Data Analysis Figure 1 below. The title of the table is "Frequency Distribution." The heading of the first column is "Number of Children" and the heading of the second column is "Frequency."

Frequency Distribution

Number of Children

Frequency

0

3

1

5

2

7

3

6

4

3

5

1

Total

25

Data Analysis Figure 1

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