Which statistic is least affected by outliers?

Which statistic is least affected by outliers?

• A. Range
• B. Standard deviation
• C. Mean
• D. IQR

Answer: (D)

The statistic that is least affected by outliers is the interquartile range. It measures the spread of the middle half of the data by subtracting the first quartile from the third quartile. Since it relies on Q1 and Q3, which capture the central portion of the data, extreme values don’t have much influence on them. So, even if you add a very large or very small value, the IQR often stays the same, reflecting the staying power of the central spread. In contrast, the range depends on the extreme values (the smallest and largest), so a single outlier can drastically change it. The mean uses every data point, so outliers pull it toward themselves, shifting the average. The standard deviation measures how spread out all values are around the mean, and outliers increase that spread by pulling the mean and pulling the deviations larger.

The statistic that is least affected by outliers is the interquartile range. It measures the spread of the middle half of the data by subtracting the first quartile from the third quartile. Since it relies on Q1 and Q3, which capture the central portion of the data, extreme values don’t have much influence on them. So, even if you add a very large or very small value, the IQR often stays the same, reflecting the staying power of the central spread.

In contrast, the range depends on the extreme values (the smallest and largest), so a single outlier can drastically change it. The mean uses every data point, so outliers pull it toward themselves, shifting the average. The standard deviation measures how spread out all values are around the mean, and outliers increase that spread by pulling the mean and pulling the deviations larger.