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By Alvan R Feinstein

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A simple mnemonic for remembering the location of the three indexes in a skewed distribution is that they are arranged both statistically and alphabetically starting at the skewed end of the data. 5 Customary location of mode, median, and mean in a right-skewed distribution. 6 VALUES IN DATA Advantages of the Median The median has four main descriptive advantages as an index of central tendency. It is better than the mean for summarizing eccentric distributions; it can also be properly used, unlike the mean, for ordinal data; it is often, unlike the mean, an actual member of the data set; and it can be applied, also unlike the mean, to sets containing incomplete longitudinal data.

The proportions are easy to determine because each member of a set of n items occupies a 1/n proportion of the data. The ranking can be done in either direction — from low values toward high, or vice versa — but as the ranks ascend (or descend), the proportions accumulate so that the first r ranks will occupy r/n of the data. 018 of the data. 696 of the data. 1 Problems in Identification The concept is easy to describe and understand, but its application produces three tricky problems: shared boundaries, intra-item percentiles, and shared ranks.

If any of the data values is 0, the entire product is 0, and the geometric mean must be 0. If the product of the data values is negative, a logarithm cannot be determined and the Nth root of the product (even if calculatable) may be meaningless. A different kind of problem occurs if the data are skewed to the left, rather than rightward. For example, suppose the data set contains the values 1, 62, 67, 67, and 75. 1, which is farther from the median than the arithmetic mean. 97 would be closer to the median of 67.

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