What is 'Symmetrical Distribution'

Symmetrical distribution occurs when the values of variables occur at regular frequencies and the mean, median and mode occur at the same point. In graph form, symmetrical distribution often appears as a bell curve. If a line were drawn dissecting the middle of the graph, it would show two sides that mirror each other.

BREAKING DOWN 'Symmetrical Distribution'

Symmetrical distribution, commonly known as symmetric distribution or normal distribution, is typically unimodal, meaning it shows only one peak in graph form. Bimodal distribution is possible as well; this type of graph has two peaks and shows two bell curve shapes located side by side. Similar to a unimodal's appearance, the two sides of the graph mirror each other, but only the mean and median occur at the same point, i.e., the center of the graph. The modes occur at two points, i.e., the highest point in each of the two bell curve graphs.

Symmetric distributions can be multimodal as well, with multiple peaks as long as the two sides of the graph mirror each other. The tails of the bell curve are the portions of the graph to the right and left. The tails illustrate the skewness of the data set. In a symmetric distribution, the data set has zero skewness.

Symmetrical Distribution vs Asymmetrical Distribution

Opposite symmetrical distribution is asymmetrical distribution. A distribution is asymmetric if it is not symmetric with zero skewness; in other words, it does not skew. An asymmetric distribution is either left-skewed or right-skewed. A left-skewed distribution, what is known as a negative distribution, has a longer left tail. A right-skewed distribution, or a positively skewed distribution, has a longer right tail. Determining whether the mean is positive or negative is important when analyzing the skew of a data set because it affects data distribution analysis.

Skewness is often an important component of a trader’s analysis of a potential investment return. A symmetric distribution of returns is evenly distributed around the mean. An asymmetric distribution with a positive right skew indicates that historical returns that deviated from the mean were primarily concentrated on the bell curve’s left side. Conversely, a negative left skew shows historical returns deviating from the mean concentrated on the right side of the curve. 

A common investment refrain is that past performance does not guarantee future results; however, past performance can illustrate patterns of return and provide insight for investors looking to make a decision about an investment.

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