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Measures of DispersionWhile central measures describe the central values (mean, median, and mode) of the sample, the dispersion measures provide description of the spread in the data. So far we have seen Range, Quantiles, Percentiles, and Interquartiles Range. Mean Absolute Deviation (MAD): A simple measure of variability is the mean absolute deviation: MAD = The mean absolute deviation is widely used as a performance measure to assess the quality of forecasting techniques. For example, how well a forecasting technique (or a forecasting model) performed in predicting a future event. For example, let us say, we are interested in assessing the skill of a weather model in predicting tomorrow's weather. So we calculate the MAD value, the mean absolute deviation between the forecast and actual values. The smaller the value of MAD, the higher the skill of the weather model in predicting tomorrow's weather . However, MAD does not lend itself to further use in making inference; moreover, even in the error analysis studies, the variance is preferred since variances of independent (i.e., uncorrelated) errors are additive; however MAD does not have such a nice feature. Variance: An important measure of variability is variance. Variance is the average of the squared deviations of each observation in the set from the arithmetic mean of all of the observations.
Variance = S 2 ; where S is the standard deviation given by
The variance is a measure of spread or dispersion among values in a data set. Therefore, the greater the variance, the more scattered the observations are around mean. For example, if the observations are made about a particular product, say an electrical appliance, then the larger variance might mean poor quality of the products coming out of the production line.
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