Any value that is smaller (or larger) than ______ standard deviations below (above) the mean is considered a statistical outlier.

• A. Two
• B. Three
• C. One
• D. Four

Answer: (A)

In statistics, you identify unusual values by measuring how far they are from the center of the data in units of standard deviation. The threshold here uses two standard deviations: any value below mean minus two standard deviations or above mean plus two standard deviations is flagged as an outlier. The reason this works well is that, for a roughly normal distribution, about 95% of observations fall within ±2 standard deviations of the mean. So values beyond that range are unusually far from the center and deserve attention as potential outliers. If you used only one standard deviation, you'd label around a third of the data as outliers in a normal distribution; if you used three standard deviations, you'd be much more conservative and fewer observations would be flagged. Four standard deviations would be even rarer. Keep in mind this rule assumes the data are approximately normal; for skewed or non-normal data, other methods (like the IQR rule) may be more appropriate.