# 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.

References in periodicals archive ?
Their topics include understanding data distributions with tables and graphs, measures of dispersion, point estimate and confidence intervals, testing hypotheses with categorical data, hypothesis tests involving three or more population means: analysis of variance, and controlling for a third variable multiple ordinary least squares regression.
Figures 3 and 4 plot measures of dispersion and skewness for the log wages and skills, respectively, of workers sorted by the firm's median-wage ventile.
Contract award: sanitation - risk management measures of dispersion of groundwater contamination site ecopole brussels cleanliness.
In quantifying the temporal trend in disparities, this study applies several measures of dispersion to the regional data on suicide rates.
They assume readers have completed at least a general introduction to statistics course, and so are profligate with such basic concepts as measures of central tendency, measures of dispersion, and standard scores.
In quantitative variables, the first measures of dispersion are variance and quasi-variance, whose expressions are reminded:
Sen (1974) divided inequality into two broad classes described as objective, or purely statistical measures of dispersion, such as Variance, the Coefficient of Variation, the Lorenz Curve and the Gini-Coefficient.
Chapter eight explains and demonstrates measures of central tendency (mode, median, and mean) and measures of dispersion (standard deviation and the normal distribution).
The three measures of dispersion ([d.sub.001], Exfoliation, and Aggregates) in Table 4 show no clear correlation between the relative exfoliation and [d.sub.001].
The data could be stored in a spreadsheet, and measures of dispersion and central tendency calculated to describe the results.
The second chapter, "A Few Basics," explains introductory statistical methods such as measures of dispersion, measures of central tendency, and sampling.
If the individual scores are similar, measures of dispersion or variability are small and the sample is relatively homogeneous in terms of those scores.

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The text passage provides definitions and explanations for various measures of dispersion in statistics, such as range, variance, standard deviation, standard error, skew, and kurtosis. It does not contain any specific mathematical questions or answers to such questions.
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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.

References in periodicals archive ?
Their topics include understanding data distributions with tables and graphs, measures of dispersion, point estimate and confidence intervals, testing hypotheses with categorical data, hypothesis tests involving three or more population means: analysis of variance, and controlling for a third variable multiple ordinary least squares regression.
Figures 3 and 4 plot measures of dispersion and skewness for the log wages and skills, respectively, of workers sorted by the firm's median-wage ventile.
Contract award: sanitation - risk management measures of dispersion of groundwater contamination site ecopole brussels cleanliness.
In quantifying the temporal trend in disparities, this study applies several measures of dispersion to the regional data on suicide rates.
They assume readers have completed at least a general introduction to statistics course, and so are profligate with such basic concepts as measures of central tendency, measures of dispersion, and standard scores.
In quantitative variables, the first measures of dispersion are variance and quasi-variance, whose expressions are reminded:
Sen (1974) divided inequality into two broad classes described as objective, or purely statistical measures of dispersion, such as Variance, the Coefficient of Variation, the Lorenz Curve and the Gini-Coefficient.
Chapter eight explains and demonstrates measures of central tendency (mode, median, and mean) and measures of dispersion (standard deviation and the normal distribution).
The three measures of dispersion ([d.sub.001], Exfoliation, and Aggregates) in Table 4 show no clear correlation between the relative exfoliation and [d.sub.001].
The data could be stored in a spreadsheet, and measures of dispersion and central tendency calculated to describe the results.
The second chapter, "A Few Basics," explains introductory statistical methods such as measures of dispersion, measures of central tendency, and sampling.
If the individual scores are similar, measures of dispersion or variability are small and the sample is relatively homogeneous in terms of those scores.

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Open / Close
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The text passage provides definitions and explanations for various measures of dispersion in statistics, such as range, variance, standard deviation, standard error, skew, and kurtosis. It does not contain any specific mathematical questions or answers to such questions.

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