What makes data skewed

A "skewed right" distribution is one in which the tail is on the right side. A "skewed left" distribution is one in which the tail is on the left side.

The above histogram is for a distribution that is skewed right. Skewed distributions bring a certain philosophical complexity to the very process of estimating a "typical value" for the distribution. To be specific, suppose that the analyst has a collection of values randomly drawn from a distribution, and wishes to summarize these observations by a "typical value". What does typical value mean? If the distribution is symmetric, the typical value is unambiguous-- it is a well-defined center of the distribution.

For example, for a bell-shaped symmetric distribution, a center point is identical to that value at the peak of the 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. Note that the mean will always be to the right of the median.

Graph A is skewed right, while Graph B is skewed left. With right-skewed graphs, the mean always comes to the right of the mode i. These features ultimately make it difficult to assign a typical value as there is no clear center point on a right-skewed graph.

By contrast, with normal distribution, because the mean, median, and mode are all equal and come at the center of the data set, you can easily use this value to more accurately generalize the data. Data skewed to the right is usually a result of a lower boundary in a data set whereas data skewed to the left is a result of a higher boundary.

So if the data set's lower bounds are extremely low relative to the rest of the data, this will cause the data to skew right. Another cause of skewness is start-up effects.

For example, if a procedure initially has a lot of successes during a long start-up period, this could create a positive skew on the data. On the opposite hand, a start-up period with several initial failures can negatively skew data.

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What Does Skewed Right Mean? Example of a right-skewed histogram.