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In-Depth Information
2.4 THE MEDIAN AS A MEASURE OF CENTRAL TENDENCY
2.4.1 GENERAL CONCEPTION OF THE MEDIAN
A second type of measure of central tendency is called the
median
.The
median is the midpoint or middle score when the scores are arranged from
lowest to highest; defined in terms of percentiles (the proportion of scores
in the distribution lower in value), the median is the fiftieth percentile.
The median can be a particularly useful index of central tendency
when a group of scores contains extreme values or
outliers
.Outliersare
sometimes found when working with income or age data. For example,
suppose in a small graduate seminar with five students we observed the
following age distribution: 21, 22, 23, 24, and 62. The mean for the class
is
40 years of age. However, does this computed
mean truly represent the “center” of the ages in the class? The answer
is “not really.” The one older student, the value of age that we judge
to be an outlier, has pulled or affected the mean such that it no longer
represents the typical student age. A better indicator of student age is the
median, which is 23 in this example. The point to remember is that the
median can compensate for high or low outlying scores in a distribution of
scores.
Y
/
n
=
152
/
5
=
30
.
2.4.2 CALCULATION OF THE MEDIAN
Calculating the median is straightforward when there is an odd number
of scores. You simply arrange the scores in ascending order and the score
in the middle is the median. When there is an even number of scores you
have, in effect, two middle scores, and the median is the average or mean
of these two scores. For example, let's modify our previous example to
include one additional student who is twenty-five years old. The group of
scores would thus be: 21, 22, 23, 24, 25, and 62. In this case, the mean is
Y
/
n
=
177
/
6
=
29
.
5, and the median is 23
+
24
=
47
/
2
=
23
.
5.
2.5 THE MODE AS A MEASURE OF CENTRAL TENDENCY
One last measure of central tendency is the
mode
. The mode is defined as
the most common or frequent value in a distribution of scores. No special
computation is involved in determining the mode. A simple inspection of
the frequency of occurrence of each data value is all that is required. For
example, the most frequent or modal happiness score in Table 2.2 is 2. In
this particular example, the mode and median are the same; that is, both
are 2 with a mean of 1.86.
The mode is particularly useful in describing nominal level data. Are
there more Republicans, Democrats, or Independents present at a par-
ticular meeting? Who is the most typical or modal mental health service
provider for a given community mental health client who is being pro-
vided mental health services by a variety of providers (e.g., psychiatrist,
