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

Responses

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

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

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

The mean and median are sometimes the same.

1 answer

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

The mean and median are sometimes the same.

While skewed data typically results in the mean being different from the median (with the mean being pulled in the direction of the skew), it is possible for the two to be equal in certain cases (for example, if the skewness is negligible or if there are specific values that balance them out). In cases of perfectly symmetrical distributions, the mean and median are indeed the same, even under conditions where there are outliers that might suggest skewness. However, in most cases involving skewed distributions, the mean will differ from the median.