Question

if the best measure of center for a given data set is the mean, then which of the following is most likely true?
the data distribution is not skewed.
the median is further from the tall of the skewed data distribution than the mean.
the median is not the middle data value.
the mean is further from the peak of the skewed data distribution than the median.

Explanation:

Step1: Recall properties of mean and median in skewed data

In a skewed data distribution, the mean is pulled towards the tail (outliers) while the median is the middle value. If the mean is the best measure of center, the data is likely not skewed (since for skewed data, median is better). Let's analyze each option:

• Option 1: "The data distribution is not skewed." If data is not skewed (symmetric), mean and median are close, and mean is a good measure. This is consistent.
• Option 2: "The median is further from the tail... than the mean." In skewed data, mean is closer to tail. If mean is best, data is not skewed, so this is incorrect.
• Option 3: "The median is not the middle data value." Median is always the middle value (for ordered data), so this is false.
• Option 4: "The mean is further from the peak... than the median." In non - skewed (symmetric) data, mean and median are close to peak. If mean is best, data is not skewed, so this is incorrect.

Answer:

The data distribution is not skewed. (Assuming the first option is the correct one based on the analysis. If the options are labeled, for example, if the first option is A, then the answer would be A. The data distribution is not skewed.)