Central Measures

Measures of central tendencies are nothing but the measures to describe the "central" values of a collected sample. For an ungrouped set of data these measures are: the mean, the median, and the mode.

The median is the middle value in an ordered array of observations. If there is an even number of observations in the array, the median is the average of the two middle numbers. If there is an odd number of data in the array, the median is the middle number.

The median is often used to summarize the distribution of an outcome. If the distribution is skewed, the median and the interquartile range may be better than other measures to indicate where the observed data are concentrated.

Generally, the median provides a better measure of location than the mean when there are some extremely large or small observations, that is, when the data are skewed to the right or to the left.

Note that if the median is less than the mean, the data set is skewed to the right. If the median is greater than the mean, the data set is skewed to the left. The mean has two distinct advantages over the median. It is more stable, and one can compute the mean based of two samples by combining the two means.

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