An outlier is, essentially, a statistical anomaly that is usually fairly easy to recognize. It is a number, or set of numbers, that falls well outside the range of what a statistician or mathematician finds acceptable, based upon the other figures in a data set. Because an outlier is far removed from the other figures, it has the potential to skew averages.
Defining an outlier may best be explained by example. If a statistician or mathematician conducts research or a survey of some kind, and the results are as follows: 3, 15, 18, 21, 26, 31 and 58, there are two outliers. In this instance, both the 3 and the 58 would be considered outliers as they are significantly different from, or outside the scope of, the other data points.
Outliers come about for many reasons, usually relatively simple errors or omissions. For example, perhaps there was human error in transcribing the information. If, in the example given above, the 3 was simply misread should have been 13, it would not be an outlier. It may also be that a step in the process was neglected during one phase of a study but not the others. These serve as good indicators of potential problems in the data and provide researchers opportunities to closely examine the processes used to find possible shortcomings.
Determining which figures are outliers is, to a large extent, at the discretion of the statistician. This can lead to possible distortions in that the data, by discarding what are perceived as outliers, can be manipulated by the statistician to more closely resemble the desired results. Deciding that a number, or several numbers, are simply outliers can significantly change that data, perhaps corrupting it.