When comparing the means and medians of skewed data, which of the following is correct? (1 point) The mean is always greater than the median. The mean and median are sometimes the same. The mean and median are always the same. The mean and median are never the same.

To determine the correct statement regarding the means and medians of skewed data, let's analyze the properties of skewed distributions: 1. **Skewed Data**: In a skewed distribution, the data is not symmetrically distributed. It can be skewed to the left (negatively skewed) or skewed to the right (positively skewed). 2. **Mean vs. Median**: - In a **negatively skewed** distribution (left-skewed), the mean is typically less than the median. - In a **positively skewed** distribution (right-skewed), the mean is typically greater than the median. 3. **Comparison**: - The mean and median can be the same in a perfectly symmetrical distribution, but in skewed distributions, they are generally not equal. - Therefore, the mean and median are not always the same, nor are they always different. Based on this analysis, the correct statement is: - **The mean is always greater than the median.** (This is only true for positively skewed data.) - **The mean and median are sometimes the same.** (This is true for symmetrical data, not skewed.) - **The mean and median are always the same.** (This is false for skewed data.) - **The mean and median are never the same.** (This is also false for symmetrical data.) Thus, the most accurate statement regarding skewed data is: **The mean and median are sometimes the same.** However, if we strictly consider skewed data, the best choice would be that the mean is not equal to the median, but the options provided do not reflect that accurately. Therefore, the answer is nuanced based on the context of skewness.