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.

Mean, Median, or Mode? What is the right choice? Well, it depends on what we are looking to do with the data at hand.

The first consideration is the type of data. If the variable is categorical, then the mode is the single measure that best describes that data.

The second consideration in selecting the central measure is to ask whether the total of all observations is of any interest. If the answer is yes, then the mean is the proper measure of the central tendency.

If the total is of no interest, then depending on whether the histogram is symmetric or skewed one must use either mean or median, respectively.

Note in all cases the histogram must be unimodal. This means the histogram should have only one mode. Do not be alarmed about the terms "histogram" and "skewed", if you have not heard of them before.

An histogram is a plot of frequencies against the categories (bins) of the entire data. The skewness refers to the nature of the frequency curve: it could be narrower and sharper on the one side; and broader and flatter on the other side. We will study histograms in the Probability Distributions section.

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