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measures of
dispersion
measures of dispersion
the different ways of calculating the extent to which a set of observations, numbers, etc., are clustered
together round a central point. Measures of dispersion are closely related to MEASURES OF CENTRAL
TENDENCY. There are six measures: the range, variance, standard deviation, standard error, skew, and
kurtosis.
The range is the simplest measure of dispersion; it relates to the actual spread of values and is equal to
the maximum less the minimum value.
The variance is a measure of the dispersion of a set of values from the mean, and should only be used
with interval-level measures. It measures the extent to which individual values are clustered around the
mean. It is calculated by averaging the squared deviations from the mean, and in so doing it takes into
account both negative values and the existence of unduly low and unduly high values. A low variance
suggests that there is a high degree of homogeneity in the value and high variance is an indication of a
low degree of homogeneity.
The standard deviation is simply the square root of the variance. It is used in preference to the variance
because it is easier to interpret, having a value in the range of the values from which it is derived.
The standard error is an estimation of the extent to which the mean of a given set of scores drawn from a
sample differs from the true mean score of the whole population. It should only be used with interval-level
measures.
The skew attempts to estimate the extent to which a set of measures deviates from the symmetry of a
normal distribution curve, whether to the left or the right. Where measures tend to be located to the right
of the curve its value is negative.
The kurtosis shows the extent to which the ‘curve’ of a set of observations is flatter or more peaked than
the normal distribution, whose kurtosis is zero. A peaked (narrower) distribution has a positive value and
a flatter curve has a negative value.
Collins Dictionary of Sociology, 3rd ed. © HarperCollins Publishers 2000
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