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psychologist, social worker, marriage and family therapist, case manager)?
Because the mode is typically not used when working with quantitative
dependent variables, it will not be emphasized in this text.
2.6 RANGE AS A MEASURE OF VARIABILITY
As we have seen, measures of central tendency (the mean, the median, and
the mode) provide information of the most typical value in a distribution
of scores. Other indicators - the range, variance, and standard deviation -
are designed to describe the diversity or variability of scores in a dis-
tribution. Perhaps the simplest measure of variability is the range ; this
measure represents what we ordinarily denote by the term in common
language. The range is a single value computed as the highest score (the
maximum score) minus the lowest score (the minimum score). In our
previous student age example, the age range is 41 (62
41). The
range is a global and relatively imprecise measure of variability for at least
two reasons: (a) it takes into account only the two scores at the extremes
of the distribution, and (b) a given range, say 41, can be associated with
very different minima and maxima (e.g., subtracting ages 62 and 21 and
subtracting ages 92 and 51 both yield the same age range). Range is used
relatively infrequently in the behavioral and social sciences.
21
=
2.7 VARIANCE AS A MEASURE OF VARIABILITY
2.7.1 GENERAL CONCEPTION OF THE VARIANCE
A very useful index of the dispersion of scores within a distribution is
called the “variance” (symbolized as s 2 ) and is crucial to all the subsequent
computational work we do in this text. The variance tells us how dispersed
the scores are with respect to the mean. Larger variances represent greater
spreads or variability of the scores from the mean. In practice, we will
see that the variance is an average of the squared deviations from the
mean.
We will show you how to compute the variance with two different
formulas that arrive at the same answer. The first is known as the defining
or deviational formula and the second is the computational formula .The
first formula is intuitive, making clear exactly how the variance can be
conceptualized. The latter formula may be computationally more conve-
nient with larger data sets but makes it somewhat harder to “see” what is
represented conceptually by the variance.
In both computational strategies, the variance is calculated in a two-
step process. The first step is to calculate what is called the sum of squares ,
or SS , which becomes the numerator of the variance formula. The second
step is to create a denominator that adjusts the sum of squares, called the
degrees of freedom ,or df .
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