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

SECTION 4.2 | Defining Standard Deviation and Variance 103
the range is 5 points. By this definition, when the scores are all whole numbers, the range
can be obtained by
X max
2 X min
1 1
Using either definition, the range is probably the most obvious way to describe how
spread out the scores are—simply find the distance between the maximum and the minimum
scores. The problem with using the range as a measure of variability is that it is
completely determined by the two extreme values and ignores the other scores in the distribution.
Thus, a distribution with one unusually large (or small) score will have a large range
even if the other scores are all clustered close together.
Because the range does not consider all the scores in the distribution, it often does not
give an accurate description of the variability for the entire distribution. For this reason, the
range is considered to be a crude and unreliable measure of variability. Therefore, in most
situations, it does not matter which definition you use to determine the range.
LEARNING CHECK
1. Which of the following sets of scores has the greatest variability?
a. 2, 3, 7, 12
b. 13, 15, 16, 17
c. 24, 25, 26, 27
d. 42, 44, 45, 46
2. What is the range for the following set of scores? 3, 7, 9, 10, 12
a. 3 points
b. 4 or 5 points
c. 9 or 10 points
d. 12 points
3. How many scores in the distribution are used to compute the range?
a. only 1
b. 2
c. 50% of them
d. all of the scores
ANSWERS
1. A, 2. C, 3. B
4.2 Defining Standard Deviation and Variance
LEARNING OBJECTIVES
3. Define variance and standard deviation and describe what is measured by each.
4. Calculate variance and standard deviation for a simple set of scores.
5. Estimate the standard deviation for a set of scores based on a visual examination of
a frequency distribution graph of the distribution.
The standard deviation is the most commonly used and the most important measure of
variability. Standard deviation uses the mean of the distribution as a reference point and
measures variability by considering the distance between each score and the mean.