In the context of probability and statistics, what does it mean if a statistic is resistant?

• A. It is not significantly affected by extreme values or outliers in the data set.
• B. It is calculated only from the $\mathrm{mean}$ of the data.
• C. It always increases as the $\mathrm{sample}\mathrm{size}$ increases.
• D. It can only be used with categorical data.

Answer: (A)

Verified step by step guidance

1. Understand that in statistics, a 'statistic' refers to a numerical summary calculated from sample data, such as the mean, median, or standard deviation.
2. Recognize that some statistics are sensitive to extreme values or outliers, meaning their values can be heavily influenced by unusually large or small data points.
3. Learn that a 'resistant' statistic is one that is not significantly affected by these extreme values or outliers, maintaining stability even when such values are present.
4. Examples of resistant statistics include the median and interquartile range, which remain relatively unchanged by outliers, unlike the mean or standard deviation.
5. Therefore, when a statistic is described as resistant, it means it provides a reliable summary of the data's central tendency or spread without being distorted by extreme observations.