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.

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