When comparing the means and medians of skewed data, the following is correct:
The mean is always greater than the median. (This statement is not correct; it depends on the direction of the skew.)
In skewed distributions:
- For positively skewed data (right skewed), the mean is usually greater than the median.
- For negatively skewed data (left skewed), the mean is usually less than the median.
Thus, the correct interpretation is that the mean and median can differ based on the direction of skewness.
Regarding the other statements:
- The mean and median are sometimes the same. (This is true for symmetric distributions but not applicable to skewed data.)
- The mean and median are always the same. (This is not true for skewed data.)
- The mean and median are never the same. (This is also incorrect, as they can be the same in symmetric distributions.)
In summary, the mean and median can differ due to skewness, but they may also be the same in symmetric distributions. The most accurate statement among your options regarding skewed data would be that the mean tends to differ from the median depending on the skewness direction.