21.01.2022 Views

Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

Statistics is one of the most practical and essential courses that you will take, and a primary goal of this popular text is to make the task of learning statistics as simple as possible. Straightforward instruction, built-in learning aids, and real-world examples have made STATISTICS FOR THE BEHAVIORAL SCIENCES, 10th Edition the text selected most often by instructors for their students in the behavioral and social sciences. The authors provide a conceptual context that makes it easier to learn formulas and procedures, explaining why procedures were developed and when they should be used. This text will also instill the basic principles of objectivity and logic that are essential for science and valuable in everyday life, making it a useful reference long after you complete the course.

Statistics is one of the most practical and essential courses that you will take, and a primary goal of this popular text is to make the task of learning statistics as simple as possible. Straightforward instruction, built-in learning aids, and real-world examples have made STATISTICS FOR THE BEHAVIORAL SCIENCES, 10th Edition the text selected most often by instructors for their students in the behavioral and social sciences. The authors provide a conceptual context that makes it easier to learn formulas and procedures, explaining why procedures were developed and when they should be used. This text will also instill the basic principles of objectivity and logic that are essential for science and valuable in everyday life, making it a useful reference long after you complete the course.

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

108 CHAPTER 4 | Variability

2. What is the variance for the following set of scores? 2, 2, 2, 2, 2

a. 0

b. 2

c. 4

d. 5

3. Which of the following values is the most reasonable estimate of the standard

deviation for the set of scores in the following distribution? (It may help to imagine

or sketch a histogram of the distribution.)

a. 0

b. 1

c. 3

d. 5

X

f

5 1

4 2

3 4

2 2

1 1

ANSWERS

1. B, 2. A, 3. B

4.3 Measuring Variance and Standard Deviation for a Population

LEARNING OBJECTIVES

6. Calculate SS, the sum of the squared deviations, for a population using either the

definitional or the computational formula and describe the circumstances in which

each formula is appropriate.

7. Calculate the variance and the standard deviation for a population.

The concepts of standard deviation and variance are the same for both samples and populations.

However, the details of the calculations differ slightly, depending on whether you

have data from a sample or from a complete population. We first consider the formulas for

populations and then look at samples in Section 4.4.

■ The Sum of Squared Deviations (SS)

Recall that variance is defined as the mean of the squared deviations. This mean is computed

exactly the same way you compute any mean: first find the sum, and then divide by

the number of scores.

sum of squared deviations

Variance 5 mean squared deviation 5

number of scores

The value in the numerator of this equation, the sum of the squared deviations, is a basic

component of variability, and we will focus on it. To simplify things, it is identified by the

notation SS (for sum of squared deviations), and it generally is referred to as the sum of

squares.

DEFINITION

SS, or sum of squares, is the sum of the squared deviation scores.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!