Question

When comparing the means and medians of skewed data, which of the following is correct?(1 point)
Responses

The mean is always greater than the median.
The mean is always greater than the median.

The mean and median are sometimes the same.
The mean and median are sometimes the same.

The mean and median are never the same.
The mean and median are never the same.

The mean and median are always the same.

Answer 1

When comparing the means and medians of skewed data, the correct response is:

**The mean is always greater than the median.**

This statement is generally true when data is positively skewed (right-skewed), while for negatively skewed (left-skewed) data, the mean is typically less than the median. Therefore, none of the provided options are universally correct as they imply absolute relationships.

However, if we are looking for a general tendency for skewed data:

- In positively skewed data, the mean is greater than the median.
- In negatively skewed data, the mean is less than the median.

It’s important to note that the mean and median can be the same in symmetric distributions, but in skewed distributions, they typically differ. Thus, the most accurate interpretation of the provided statements would be that they are skewed in the context but have exceptions.