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

94 CHAPTER 3 | Central Tendency
LEARNING CHECK
1. Which of the following is true for a symmetrical distribution?
a. the mean, median, and mode are all equal
b. mean = median
c. mean = mode
d. median = mode
2. For a negatively skewed distribution with a mode of X = 25 and a median of 20, the
mean is probably _____.
a. greater than 25
b. less than 20
c. between 20 and 25
d. cannot be determined from the information given
3. A distribution is positively skewed. Which is the most probable order for the three
measures of central tendency?
a. mean = 40, median = 50, mode = 60
b. mean = 60, median = 50, mode = 40
c. mean = 40, median = 60, mode = 50
d. mean = 50, median = 50, mode = 50
ANSWERS
1. B, 2. B, 3. B
SUMMARY
1. The purpose of central tendency is to determine the
single value that identifies the center of the distribution
and best represents the entire set of scores. The
three standard measures of central tendency are the
mode, the median, and the mean.
2. The mean is the arithmetic average. It is computed
by adding all the scores and then dividing by
the number of scores. Conceptually, the mean is
obtained by dividing the total (SX) equally among
the number of individuals (N or n). The mean can
also be defined as the balance point for the distribution.
The distances above the mean are exactly balanced
by the distances below the mean. Although the
calculation is the same for a population or a sample
mean, a population mean is identified by the symbol
μ, and a sample mean is identified by M. In most
situations with numerical scores from an interval or
a ratio scale, the mean is the preferred measure of
central tendency.
3. Changing any score in the distribution causes the
mean to be changed. When a constant value is added
to (or subtracted from) every score in a distribution,
the same constant value is added to (or subtracted
from) the mean. If every score is multiplied by
a constant, the mean is multiplied by the same
constant.
4. The median is the midpoint of a distribution of scores.
The median is the preferred measure of central tendency
when a distribution has a few extreme scores
that displace the value of the mean. The median also
is used when there are undetermined (infinite) scores
that make it impossible to compute a mean. Finally,
the median is the preferred measure of central tendency
for data from an ordinal scale.
5. The mode is the most frequently occurring score in a
distribution. It is easily located by finding the peak in
a frequency distribution graph. For data measured on
a nominal scale, the mode is the appropriate measure