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

SECTION 4.4 | Measuring Standard Deviation and Variance for a Sample 111
Earlier, in Examples 4.4 and 4.5, we computed the sum of squared deviations for a simple
population of N 5 4 scores (1, 0, 6, 1) and obtained SS 5 22. For this population, the variance is
s 2 5 SS
N 5 22 4 5 5.50
and the standard deviation is s5Ï5.50 5 2.345
LEARNING CHECK
1. What is the value of SS, the sum of the squared deviations, for the following population
of N 5 4 scores? Scores: 1, 4, 6, 1
a. 0
b. 18
c. 54
d. 12 2 5 144
2. Each of the following is the sum of the scores for a population of N 5 4 scores. For
which population would the definitional formula be a better choice than the computational
formula for calculating SS.
a. SX 5 9
b. SX 5 12
c. SX 5 15
d. SX 5 19
3. What is the standard deviation for the following population of scores?
Scores: 1, 3, 7, 4, 5
a. 20
b. 5
c. 4
d. 2
ANSWERS
1. B, 2. B, 3. D
4.4 Measuring Standard Deviation and Variance for a Sample
LEARNING OBJECTIVES
8. Explain why it is necessary to make a correction to the formulas for variance and
standard deviation when computing these statistics for a sample.
9. Calculate SS, the sum of the squared deviations, for a sample using either the
definitional or the computational formula and describe the circumstances in which
each formula is appropriate.
10. Calculate the variance and the standard deviation for a sample.
■ The Problem with Sample Variability
The goal of inferential statistics is to use the limited information from samples to draw general
conclusions about populations. The basic assumption of this process is that samples should be