Why does skewness happen

The first distribution shown has a positive skew. This means that it has a long tail in the positive direction. The distribution below it has a negative skew since it has a long tail in the negative direction. Finally, the third distribution is symmetric and has no skew. Skew 2 of 3 Distributions with positive skews are more common than distributions with negative skews.

One example is the distribution of income. Skewness is a measure of the symmetry of a distribution. The highest point of a distribution is its mode. The mode marks the response value on the x-axis that occurs with the highest probability.

A distribution is skewed if the tail on one side of the mode is fatter or longer than on the other: it is asymmetrical. In an asymmetrical distribution a negative skew indicates that the tail on the left side is longer than on the right side left-skewed , conversely a positive skew indicates the tail on the right side is longer than on the left right-skewed.

Asymmetric distributions occur when extreme values lead to a distortion of the normal distribution. For a skewed distribution, however, there is no "center" in the usual sense of the word. Be that as it may, several "typical value" metrics are often used for skewed distributions. The first metric is the mode of the distribution. Unfortunately, for severely-skewed distributions, the mode may be at or near the left or right tail of the data and so it seems not to be a good representative of the center of the distribution.

As a second choice, one could conceptually argue that the mean the point on the horizontal axis where the distributiuon would balance would serve well as the typical value. For symmetric distributions, the conceptual problem disappears because at the population level the mode, mean, and median are identical.

For skewed distributions, however, these 3 metrics are markedly different. In practice, for skewed distributions the most commonly reported typical value is the mean; the next most common is the median; the least common is the mode. Because each of these 3 metrics reflects a different aspect of "centerness", it is recommended that the analyst report at least 2 mean and median , and preferably all 3 mean, median, and mode in summarizing and characterizing a data set.

Skewed data often occur due to lower or upper bounds on the data. That is, data that have a lower bound are often skewed right while data that have an upper bound are often skewed left. Skewness can also result from start-up effects.