Question

mpare the values. choose the correct answer below. a. the median, 10% trimmed mean, and 20% trimmed mean are close to each other. however, the untrimmed mean is significantly different from those values. b. the median, untrimmed mean, and 20% trimmed mean are close to each other. however, the 10% trimmed mean is significantly different from those values. c. the untrimmed mean, 10% trimmed mean, and 20% trimmed mean are close to each other. however, the median is significantly different from those values. d. all of the values are close to each other. e. the median, untrimmed mean, and 10% trimmed mean are close to each other. however, the 20% trimmed mean is significantly different from those values.

Explanation:

To solve this, we analyze the behavior of trimmed means, median, and untrimmed mean:

• Trimmed means (10% and 20%) and the median are robust to outliers (they reduce the impact of extreme values).
• The untrimmed mean is sensitive to outliers. If there are outliers, the untrimmed mean will differ from the median and trimmed means, while the median and trimmed means (10% and 20%) will be close (as they all mitigate outlier effects).

Trimmed means (10%, 20%) and median are robust to outliers, so they cluster. The untrimmed mean is sensitive to outliers, so it differs from them. This matches option A.

Answer:

A. The median, 10% trimmed mean, and 20% trimmed mean are close to each other. However, the untrimmed mean is significantly different from those values.