Using the IQR rule, which values are considered outliers?

• A. Values below Q1 − 2 IQR or above Q3 + 2 IQR
• B. Values beyond the outer fences
• C. Values below Q1 − 1.5 IQR or above Q3 + 1.5 IQR
• D. All observations within the middle 50% are outliers

Answer: (C)

Outliers identified with the IQR rule are values that lie far away from the central portion of the data. The IQR is the spread of the middle 50% of the data, computed as IQR = Q3 − Q1, where Q1 and Q3 are the 25th and 75th percentiles. The standard rule flags any observation below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times the IQR as an outlier. This threshold focuses on points that are unusually far from the central box in a boxplot, capturing typical and moderate outliers.

The option using 1.5 times the IQR matches this common rule, making it the best choice. Using 2 times the IQR would identify a different, less standard threshold, and describing all observations within the middle 50% as outliers contradicts what the IQR rule measures. Values beyond the outer fences (3×IQR) are considered extreme outliers, which is a related but separate idea from the basic IQR rule.