Which of the following is not necessarily an outlier in a data set?

• A. A value that is more than $1.5$ times the interquartile range above the third quartile
• B. A value that is less than the first quartile minus $1.5$ times the interquartile range
• C. A value that is extremely far from the mean compared to other data points
• D. A value that is equal to the $\mathrm{median}$

Answer: (D)

Verified step by step guidance

1. Understand the definition of an outlier in the context of the interquartile range (IQR). Typically, a data point is considered an outlier if it lies more than 1.5 times the IQR above the third quartile (Q3) or below the first quartile (Q1).
2. Recognize that the first two options describe values that meet this IQR-based criterion for outliers: values greater than \(Q3 + 1.5 \times IQR\) or less than \(Q1 - 1.5 \times IQR\) are classified as outliers.
3. Consider the third option, which refers to values that are extremely far from the mean compared to other data points. This is a common informal way to identify outliers, often using standard deviations, so such values are generally considered outliers.
4. Analyze the fourth option, a value equal to the median. The median is the middle value of a data set and by definition lies within the central part of the data distribution, so it is not necessarily an outlier.
5. Conclude that the value equal to the median is not necessarily an outlier, while the other options describe values that meet common criteria for outliers.