Understanding Psychology (10th Ed)

FIGURE 2 
In this histogram, the number of students obtaining each score is represented 
by a bar.
FIGURE 1 
Example of a frequency 
distribution, which arranges scores from 
a sample and indicates how often a 
particular score is present.
Test
Number of Students
 Score
Attaining That Score
96
1
92
1
90
2
89
1
86
2
85 
2
83 
2
80
1
78 
3
73 
1
72 
2
69 
2
59
1
58
1
49
1
A Sample Frequency Distribution
3 
0 
Number of students 
50 
49 58 
59 
69 72 
73 
78 
80 
83 85 
86 
89 
90 
92 96 
80 
55 75 
70 
60 65 
85 90 
Score 
95 
1 
2 
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Module 56 
Descriptive Statistics 
A-7
The Mean: 
Finding the Middle
A measure of central tendency that is less sensitive to extreme scores than the mean 
is the median. The median is the point in a distribution of scores that divides the 
distribution exactly in half. If we arrange all the scores in order from the highest to 
the lowest, the median lies in the middle of the distribution.
For example, consider a distribution of fi ve scores: 10, 8, 7, 4, and 3. The point 
that divides the distribution exactly in half is the score 7: Two scores in the distribu-
tion lie above the 7 score, and two scores lie below it. If there are an even number 
of scores in a distribution—in which case there will be no score lying in the middle—
the two middle scores are averaged. If our distribution consisted of scores of 10, 8, 
7, 6, 4, and 3, then, we would average the two middle scores of 7 and 6 to form a 
median of 7 
1
6 divided by 2, or 13/2 
5 
6.5. 
In our original sample test scores, there are 23 scores. The score that divides the 
distribution exactly in half will be the 12th score in the frequency distribution of 
scores because the 12th score has 11 scores above it and 11 below it. If you count 
down to the 11th score in the distribution depicted in Figure 1, you will see that the 
score is 80. Therefore, the median of the distribution is 80. 
One feature of the median as a measure of central tendency is that it is insensi-
tive to extreme scores. For example, adding the scores of 20 and 22 to our distribution 
would change the median no more than would adding scores of 48 and 47 to the 
distribution. The reason is clear: The median divides a set of scores in half, and the 
magnitude of the scores is of no consequence in this process. 
The median is often used instead of the mean when extreme scores might be 
misleading. For example, government statistics on income are typically presented 
using the median as the measure of central tendency because the median corrects for 
the small number of extreme cases of very wealthy individuals, whose high incomes 
might otherwise infl ate the mean income.
The Mode: 
Finding What Is Most Frequent
The fi nal measure of central tendency is the mode. The mode is the most frequently 
occurring score in a set of scores. If you return to the distribution in Figure 1, you 
can see that three people scored 78, and the frequency of all the other scores is either 
2 or 1. The mode for the distribution, then, is 78.
Some distributions, of course, may have more than one score occurring most 
frequently. For instance, we could imagine that if the distribution had a score of 86 
added to the two that are already there, there would be two most frequently occur-
ring categories: 78 and now 86. In this instance, we would say there are two modes—
a case known as a bimodal distribution . 
The mode is often used as a measure of preference or popularity. For instance, 
if teachers wanted to know who was the most popular child in their elementary 
school classrooms, they might develop a questionnaire that asked the students to 
choose someone with whom they would like to participate in some activity. After the 
choices were tallied, the mode probably would provide the best indication of which 
child was the most popular.