In a normal probability distribution, the mean, median, and mode are equal and fall at the center of the distribution, with the values symmetrically distributed around the mean. Skewed probability distributions are distributions where the values are not symmetrically distributed around the mean.
If a distribution is POSITIVELY SKEWED (i.e., RIGHT-SKEWED), the mean and median are greater than (i.e., fall to the right of) the mode. This produces a distribution in which the tail on the right side is longer or fatter than the tail on the left side.
If a distribution is NEGATIVELY SKEWED (i.e., LEFT-SKEWED), the mean and median are less than (i.e., fall to the left of) the mode. This produces a distribution in which the tail on the left side is longer or fatter than the tail on the right side.
Skewness can affect the interpretation of the mean, median, and mode. For instance, in a positively skewed distribution, the mean will be higher than the median, which might give a misleading impression of the typical value if one only considers the mean. Furthermore, many statistical techniques assume that the data follows a normal distribution (i.e., no skewness). When data is skewed, these assumptions are violated, which can lead to errors in statistical inference.