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

96 CHAPTER 3 | Central Tendency
DEMONSTRATION 3.1
c. The most common error with the mode is for students to report the highest frequency
in a distribution rather than the score with the highest frequency. Remember that the
purpose of central tendency is to find the most representative score. For the distribution
in the margin, the mode is X = 3, not f = 4.
COMPUTING MEASURES OF CENTRAL TENDENCY
For the following sample, find the mean, median, and mode. The scores are:
5, 6, 9, 11, 5, 11, 8, 14, 2, 11
Compute the Mean The calculation of the mean requires two pieces of information; the
sum of the scores, SX, and the number of scores, n. For this sample, n = 10 and
SX = 5 + 6 + 9 + 11 + 5 + 11 + 8 + 14 + 2 + 11 = 82
Therefore, the sample mean is
M 5 SX
n 5 82
10 5 8.2
Find the Median To find the median, first list the scores in order from smallest to largest.
With an even number of scores, the median is the average of the middle two scores in the list.
Listed in order, the scores are:
2, 5, 5, 6, 8, 9, 11, 11, 11, 14
The middle two scores are 8 and 9, and the median is 8.5.
Find the mode For this sample, X = 11 is the score that occurs most frequently. The mode
is X = 11.
PROBLEMS
1. Find the mean, median, and mode for the following
sample of scores:
5, 4, 5, 2, 7, 1, 3, 5
2. Find the mean, median, and mode for the following
sample of scores:
3, 6, 7, 3, 9, 8, 3, 7, 5
3. Find the mean, median, and mode for the scores in the
following frequency distribution table:
X
F
6 1
5 2
4 2
3 2
2 2
1 5
4. Find the mean, median, and mode for the scores in the
following frequency distribution table:
X
f
8 1
7 1
6 2
5 5
4 2
3 2
5. For the following sample of n 5 10 scores:
a. Assume that the scores are measurements of a
discrete variable and find the median.
b. Assume that the scores are measurements of a continuous
variable and find the median by locating
the precise midpoint of the distribution.
Scores: 2, 3, 4, 4, 5, 5, 5, 6, 6, 7