How Does the Outlier Affect the Mean, Median & Mode?

The Dictionary of Statistics defines an outlier as "an observation that appears to deviate markedly from the other observations of the sample in which it appears." Statistical measures that are not highly affected by outliers are called robust.

Outlers' Effect on the Mean

Even a single outlier can have a huge effect on the mean. Consider the following data sets, the first with no outlier, the second with one relatively moderate outlier, the third with one extreme outlier and the last with several extreme outliers:

Data set 1: 150, 160, 130, 150, 120

Data set 2: 150, 160, 130, 150, 120, 180

Data set 3: 150, 160, 130, 150, 120, 350

Data set 4: 150, 160, 130, 150, 120, 300, 320, 340, 350.

Data set (DS) 1 has a mean of 142; DS 2 has a mean of 148.3, DS 3 has a mean of 176 and DS 4 has a mean of 224.

Outliers' Effect on the Median

The median, or the number that is higher than half the numbers and lower than half, is much less affected by outliers than the mean. The median for data sets 1, 2 and 3 is 150. Even for data set 4, it goes up only to 160.

Outliers' Effect on the Mode

Unless two or more of the outliers have the exact same value, the outliers will have no effect at all on the mode, which is the most common value. The mode for all the data sets is 150, because there are two cases of 150 in each data set, and no other value is repeated.

References

• "Dictionary of Statistics"; Brian Everitt; 1998

Resources

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