Which of the following is sensitive to extreme values?

Question

BlackTom AI · Accepted Answer

To begin, consider the concept of sensitivity to extreme values in a data set.
Option 1: The interquartile range. This measure focuses on the middle 50% of the data and is designed to be resistant to outliers, so it is not highly sensitive to extreme values.
Option 2: The arithmetic mean. The mean uses all data points in its calculation, so a few extreme values can pull it toward the tails of the distribution, making it inherently sensitive to outliers.
Option 3: The 1st quartile. The first quartile marks the 25th percentile and is determined by the order of the data; while it can be influenced by extreme values in small samples, its primary role is to summarize the lower portion of the data and it is generally less sensitive to extreme outliers than the mean.
Option 4: The median. The median is the middle value (or average of the two middle values) and is famous for its robustness to extreme values, since extreme observations have little effect on its position.
In summary, among the options, the statistic that is most sensitive to extreme values is the arithmetic mean, while the other options are designed to resist or are less affected by outliers.

Which of the following is sensitive to extreme values?单项选择题

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