When comparing the means and medians of skewed data, the correct statement is:
The mean is always greater than the median.
However, it's worth noting that this statement is only true for right-skewed data (positive skew), while for left-skewed data (negative skew), the mean is often less than the median. Therefore, a more nuanced understanding is that:
- In right-skewed distributions, the mean is greater than the median.
- In left-skewed distributions, the mean is less than the median.
Both the mean and median can be the same in normally distributed (symmetrical) data or very specific cases of skewed data, but this is less common.
So the best answer, if it has to be one of the provided options, would acknowledge that the relationship can vary with skewness—mathematically speaking, the mean and median are not guaranteed to be the same or one greater than the other in all instances, depending on the direction of skew. Hence, if the question is looking for a single statement to select, the wording should ideally reflect the context of skewness accurately. In terms of the usual case for heavily skewed data, the mean does tend to gravitate towards the tail in comparison to the median.