Which statistic is considered resistant to outliers?

Which statistic is considered resistant to outliers?

• A. Range
• B. Variance
• C. Interquartile range (IQR)
• D. Mean

Answer: (C)

Outliers distort measures of spread, so a resistant statistic remains fairly unchanged when extreme values appear. The interquartile range does this by focusing on the middle 50% of the data. It’s calculated as the difference between the 75th percentile and the 25th percentile, which means extreme high or low values outside the central portion don’t affect it much. In other words, the tails are ignored, keeping the IQR stable in the presence of outliers. By contrast, the range depends on the smallest and largest values, so a single outlier can drastically change it. The mean shifts toward an extreme value, and the variance (which uses squared deviations) becomes larger with outliers. So those statistics are not resistant, unlike the interquartile range.

Outliers distort measures of spread, so a resistant statistic remains fairly unchanged when extreme values appear. The interquartile range does this by focusing on the middle 50% of the data. It’s calculated as the difference between the 75th percentile and the 25th percentile, which means extreme high or low values outside the central portion don’t affect it much. In other words, the tails are ignored, keeping the IQR stable in the presence of outliers.

By contrast, the range depends on the smallest and largest values, so a single outlier can drastically change it. The mean shifts toward an extreme value, and the variance (which uses squared deviations) becomes larger with outliers. So those statistics are not resistant, unlike the interquartile range.