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

70 CHAPTER 3 | Central Tendency
(a)
(b)
f
f
1 2 3 4 5 6 7 8 9
X
1 2 3 4 5 6 7 8 9 X
(c)
f
FIGURE 3.2
Three distributions demonstrating the
difficulty of defining central tendency.
In each case, try to locate the
“center” of the distribution.
1 2 3 4 5 6 7 8 9 X
different characteristics. To decide which of the three measures is best for any particular
distribution, you should keep in mind that the general purpose of central tendency is to
find the single most representative score. Each of the three measures we present has been
developed to work best in a specific situation. We examine this issue in more detail after
we introduce the three measures.
3.2 The Mean
LEARNING OBJECTIVES
1. Define the mean and calculate both the population mean and the sample mean.
2. Explain the alternative definitions of the mean as the amount each individual receives
when the total is divided equally and as a balancing point.
3. Calculate a weighted mean.
4. Find n, SX, and M using scores in a frequency distribution table.
5. Describe how the mean is affected by each of the following: changing a score,
adding or removing a score, adding or subtracting a constant from each score, and
multiplying or dividing each score by a constant.
The mean, also known as the arithmetic average, is computed by adding all the scores in the
distribution and dividing by the number of scores. The mean for a population is identified
by the Greek letter mu, m (pronounced “mew”), and the mean for a sample is identified by
M or X (read “x-bar”).
The convention in many statistics textbooks is to use X to represent the mean for a
sample. However, in manuscripts and in published research reports the letter M is the standard
notation for a sample mean. Because you will encounter the letter M when reading