Which statistic is most robust to outliers?

Which statistic is most robust to outliers?

• A. Interquartile Range
• B. Standard Deviation
• C. Mean
• D. Range

Answer: (A)

When thinking about robustness to outliers, focus on how much a statistic changes when extreme values appear. The interquartile range measures the spread of the central 50% of the data, bounded by the 25th and 75th percentiles, so those extreme values lie outside this central region and barely affect the quartiles. This makes the IQR resistant to outliers and a reliable indicator of dispersion when data are skewed or have unusual points. In contrast, the standard deviation relies on how far every value is from the mean and squares those deviations, so a single outlier can disproportionately inflate the SD. The mean itself uses all observations, so an extreme value shifts it. The range uses only the smallest and largest values, so one outlier can dramatically expand it. So, the interquartile range is the best choice for robustness to outliers.

When thinking about robustness to outliers, focus on how much a statistic changes when extreme values appear. The interquartile range measures the spread of the central 50% of the data, bounded by the 25th and 75th percentiles, so those extreme values lie outside this central region and barely affect the quartiles. This makes the IQR resistant to outliers and a reliable indicator of dispersion when data are skewed or have unusual points.

In contrast, the standard deviation relies on how far every value is from the mean and squares those deviations, so a single outlier can disproportionately inflate the SD. The mean itself uses all observations, so an extreme value shifts it. The range uses only the smallest and largest values, so one outlier can dramatically expand it.

So, the interquartile range is the best choice for robustness to outliers.