# Symmetrical Distribution

## What is 'Symmetrical Distribution'

Symmetrical distribution is a situation in which the values of variables occur at regular frequencies, and the mean, median and mode occur at the same point. Unlike asymmetrical distribution, symmetrical distribution does not skew.

Symmetrical distribution is commonly shaped like a bell curve when depicted on a graph; if a line is drawn down the middle of the graph, the two sides mirror each other.

## BREAKING DOWN 'Symmetrical Distribution'

Symmetrical distribution is also known as symmetric distribution or normal distribution.

Bell curves represent one form of symmetrical distribution. Most symmetric distributions are unimodal, having only one peak.

A type of symmetrical distribution that is not shaped like a bell curve is a bimodal symmetric distribution. This graph has two peaks and is shaped like two bell curves placed side by side. The two sides of this graph still mirror each other, but only the mean and median occur at the same point – the center of the graph. The modes occur at two points – the highest point in each of the two bell curves. Symmetric distributions can also be multimodal with multiple peaks as long as the two sides of the graph mirror each other.

In a symmetrical distribution bell curve, the tails of the curve are the parts to the right and left. These tails indicate the skewness of the data set. In a symmetric distribution, the data set has zero skewness.

## Asymmetric Distribution

If a distribution is not symmetric with zero skewness, then it is asymmetric. Asymmetric distributions are either left-skewed or right-skewed. A left-skewed distribution has a longer left tail and is considered negatively skewed. A right-skewed distribution has a longer right tail and is considered positively skewed. In analyzing the skew of a data set, it is also important to consider whether the mean is positive or negative, as it effects the analysis of the data distribution.

Investment return data sets are often analyzed for their skewness. A symmetric distribution of returns is evenly distributed around the mean. An asymmetric distribution with a positive right skew shows that historical returns that deviated from the mean were mainly concentrated on the left side of the curve. An asymmetric distribution with a negative left skew shows that historical returns that deviated from the mean were mostly concentrated on the right side of the curve. While past performance returns are not completely indicative of future results, they can represent return pattern tendencies, which can provide insight on an investment’s return for investors.

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