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Skewed distributions have an uneven shape with a longer tail on one side of the median. They can be positively or negatively skewed, and understanding their properties is important in statistical applications. Skewed distributions do not follow standard normal patterns and have different standard deviation values for each side of the curve.
A skewed distribution refers to a probability distribution that is uneven and skewed in nature. Unlike a standard normal distribution, which resembles a bell curve in shape, skewed distributions are shifted to one side, possessing a longer tail on one side relative to the other side of the median. The other side of the curve will have a peak of clumped values where most of the data points occur. This type of distribution curve is generally classified as having a positive or a negative skew, depending on the direction of the curve’s shift.
In general, a skewed distribution is said to have a positive slope if the tail of the curve is longer on the right side compared to the left side. This skewed distribution is also known as skewed to the right because the right side has a wider spread of data points. Positive slope curves have the largest number of values towards the left side of the curve.
In contrast, negatively skewed distributions have the largest number of data points on the right side of the curve. These curves have longer tails on the left sides, so they are said to be skewed to the left. An important rule of thumb in determining the direction of bias is to consider the length of the tail rather than the location of the mean or median. This is because the bias is ultimately due to the outermost values, which extend the curve to 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 bias. However, these assumptions could 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 the standard deviation. Normal distributions imply 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 the 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 greater spread of data on that side compared to the shorter tail.
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