Understanding Psychology (10th Ed)

descriptive statistics
The branch of 
statistics that provides a means of 
summarizing data.
frequency distribution
An arrange-
ment of scores from a sample that 
indicates how often a particular score 
is present.
histogram
Bar graph.
Key Concept 
What measures can we use 
to summarize sets of data?
M O D U L E 5 6 
Descriptive Statistics 
statistics 
The branch of mathematics 
concerned with collecting, organizing, 
analyzing, and drawing conclusions 
from numerical data.
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A-6 Appendix 
Going by the Numbers: Statistics in Psychology
 
Arranging the scores from the highest to the lowest allows us to visually inspect 
the data. Most often, however, visual inspection is insuffi cient. For one thing, there 
may be so many scores in a sample that it is diffi cult to construct a meaningful visual 
representation. For another, our interpretations of patterns on a graph or table are 
often biased and inaccurate; more precise, mathematically based measures would 
seem to be preferable. In cases in which a precise means of summarizing the data is 
desirable, psychologists turn to measures of central tendency. Central tendency is an 
index of the central location within a distribution of scores. There are three major 
measures of central tendency: the mean, the median, and the mode.
The Mean: Finding the Average
The most familiar measure of central tendency is the mean. A mean is the technical term 
for an average, which is simply the sum of all the scores in a set, divided by the number 
of scores making up the set. For example, to calculate the mean of the sample we have 
been using, begin by adding each of the numbers (96 
1
92 
1
90 
1
90 
1
89 
1
. . . and 
so forth). When you have the total, divide that sum by the number of scores, which is 
23. This calculation, 1,800/23 
5
78.26 produces a mean score, or average, for our sample.
In general, the mean is an accurate refl ection of the central score in a set of scores; 
as you can see from the histogram in Figure 2, our mean of 78.26 falls roughly in the 
center of the distribution of scores. Yet the mean does not always provide the best 
measure of central tendency. For one thing, the mean is very sensitive to extreme 
scores. As an example, imagine that we added two scores of 20 and 22 to our sample 
scores. The mean would now become 1,842/25, or 73.68—a drop of almost fi ve 
points. Because of its sensitivity to extreme scores, then, the mean can sometimes 
present a deceptive picture of a set of scores, especially in cases where the mean is 
based on a relatively small number of scores.