Using the IQR method, which of the following describes outliers?

• A. Outliers are values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR.
• B. Outliers are values below Q3 − 1.5·IQR or above Q1 + 1.5·IQR.
• C. Outliers are values more than two standard deviations from the mean.
• D. Outliers are any values below the mean.

Answer: (A)

Using the IQR method, outliers are data points that lie far from the central 50% of the data. The spread of the middle half is measured by the interquartile range, IQR = Q3 − Q1. The typical boundaries are Q1 minus 1.5 times the IQR and Q3 plus 1.5 times the IQR. Any value outside those boundaries is considered an outlier because it sits well away from the main cluster of observations. This is why the description of outliers as values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR is correct. The idea of being beyond Q3 − 1.5·IQR or beyond Q1 + 1.5·IQR is reversed, so that option doesn’t describe the correct fences. The notion of being more than two standard deviations from the mean uses a different criterion based on the normal distribution, not the IQR method. And saying any value below the mean is an outlier isn’t correct, since many values below the mean can still be typical.