An outlier is an observation much larger or smaller than the rest of the data. It may be a recording error, or a real but unusual case. NIST notes that extreme values in the tails distort the mean but not the median, and recommends the median as the location estimate when such values are present. OpenStax gives the same advice.
Example
Seven monthly electricity bills: $42, $45, $47, $48, $50, $52 and $310.
- Mean = 594 ÷ 7 ≈ $84.86
- Median = $48
Without the $310 bill the mean would be 284 ÷ 6 ≈ $47.33, close to the median. The large gap between mean and median is a quick sign that an outlier is present.
Common mistakes
Deleting an outlier because it is inconvenient hides real information. Check whether it is an error first, report results with and without it, and consider the median or the standard deviation to describe spread. The guide to calculating an average shows the full example.