Using the IQR method, an outlier is defined as...

Using the IQR method, an outlier is defined as...

• A. A value above Q1 + 2·IQR
• B. A value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR
• C. A value below Q3 − 2·IQR
• D. A value more than 3 standard deviations from the mean

Answer: (B)

The idea is that outliers in the IQR method are observations that fall far from the middle 50% of the data. The middle 50% lies between the first and third quartiles, so the IQR is Q3 minus Q1. A value is considered an outlier if it lies below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times the IQR. This creates lower and upper fences that mark unusually small or large values relative to the central spread. That’s why the correct description is a value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR. The other options don’t fit this rule: using 2·IQR from Q1 isn’t the standard fence, and using 2·IQR below Q3 misplaces the boundary. Relying on the 3-standard-deviation rule is a different method based on the mean and standard deviation, not the IQR-based approach.

The idea is that outliers in the IQR method are observations that fall far from the middle 50% of the data. The middle 50% lies between the first and third quartiles, so the IQR is Q3 minus Q1. A value is considered an outlier if it lies below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times the IQR. This creates lower and upper fences that mark unusually small or large values relative to the central spread. That’s why the correct description is a value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR.

The other options don’t fit this rule: using 2·IQR from Q1 isn’t the standard fence, and using 2·IQR below Q3 misplaces the boundary. Relying on the 3-standard-deviation rule is a different method based on the mean and standard deviation, not the IQR-based approach.