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A distribution can be described in terms of its central tendency—that is, the point in the
distribution around which the data are centered—and its dispersion, or spread. The arithmetic
average, or arithmetic mean, is the most commonly used measure of central tendency. It is
computed by calculating the sum of all the scores of the variable and dividing this sum by the
number of participants in the distribution (denoted by the letter N). In the data presented
in Figure 2.5 "Height Distribution", the mean height of the students is 67.12 inches. The sample
mean is usually indicated by the letter M.
In some cases, however, the data distribution is not symmetrical. This occurs when there are one
or more extreme scores (known as outliers) at one end of the distribution. Consider, for instance,
the variable of family income (see Figure 2.6 "Family Income Distribution"), which includes an
outlier (a value of $3,800,000). In this case the mean is not a good measure of central tendency.
Although it appears from Figure 2.6 "Family Income Distribution" that the central tendency of
the family income variable should be around $70,000, the mean family income is actually
$223,960. The single very extreme income has a disproportionate impact on the mean, resulting
in a value that does not well represent the central tendency.
The median is used as an alternative measure of central tendency when distributions are not
symmetrical. The median is the score in the center of the distribution, meaning that 50% of the
scores are greater than the median and 50% of the scores are less than the median. In our case,
the median household income ($73,000) is a much better indication of central tendency than is
the mean household income ($223,960).