A normally distributed bell curve.

A skewed distribution refers to a probability distribution that is uneven and asymmetrical in nature. Unlike a standard normal distribution, which resembles a bell-shaped curve, skewed distributions are shifted to one side, having a longer tail on one side relative to the other side of the median. The other side of the curve will have a clustered peak of values where most data points occur. This type of distribution curve is generally classified as having a positive or negative slope, depending on the direction of displacement of the curve.

A distribution skewed to the right or negatively skewed.

Generally, a skewed distribution is said to have a positive slope if the tail of the curve is longer on the right side than the left side. This skewed distribution is also called right skewed because the right side has a wider range of data points. Positive slope curves have the most values towards the left side of the curve.

In contrast, distributions with negative slope have most data points on the right side of the curve. These curves have longer tails on the left sides, so they are said to be sloping to the left. An important rule of thumb for determining the direction of the slope is to consider the length of the tail rather than the location of the mean or median. This is because the slope is ultimately caused by the furthest values, which extend the curve towards that side of the graph.

Understanding the properties of a skewed distribution is important in many statistical applications. Many people assume that the data follows a bell curve, or normal distribution, so they also assume that a graph has zero distortion. These assumptions, however, can lead them to misinterpret information about the actual distribution.

A skewed distribution is inherently unequal in nature, so it will not follow standard normal patterns such as standard deviation. Normal distributions involve a standard deviation that applies to both sides of the curve, but skewed distributions will have different standard deviation values for each side of the curve. This is because the two sides are not mirror images of each other, so equations that describe one side cannot be applied to the other. The standard deviation value is generally larger for the side with the longer tail because there is a wider distribution of data on that side compared to the shorter tail.