What is the common 3-sigma rule to identify potential outliers in a normal distribution?

• A. Values beyond ±2 standard deviations from the mean are potential outliers.
• B. Values beyond ±3 standard deviations from the mean are potential outliers.
• C. Values beyond ±4 standard deviations from the mean are potential outliers.
• D. Values beyond ±1 standard deviation from the mean are potential outliers.

Answer: (B)

In a normal distribution, most values cluster near the mean, and the spread is measured by the standard deviation. The three-sigma rule says that about 99.7% of observations lie within three standard deviations of the mean. So a value that lies more than three standard deviations away from the mean—i.e., outside the interval mean minus three standard deviations to mean plus three standard deviations—is considered a potential outlier. This threshold makes sense because such points are very uncommon in a true normal distribution and stand out from the bulk of the data.

For example, if the mean is 50 and the standard deviation is 5, values outside 35 to 65 would be flagged as potential outliers. Remember, this is a rule of thumb best suited for roughly normal data; if the data are skewed or heavy-tailed, the threshold may not be as effective and alternative methods might be needed.