## 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.

Next Up

## 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.

RELATED TERMS
1. ### Probability Distribution

A probability distribution is a statistical function that describes ...
2. ### Distribution

Distribution occurs when a mutual fund, company or retirement ...
3. ### Distribution Yield

A distribution yield is a measurement of cash flow paid by an ...
4. ### Excess Kurtosis

Excess kurtosis describes a probability distribution with fat ...
5. ### Kurtosis

Kurtosis is a statistical measure used to describe the distribution ...
6. ### Horizontal Skew

Horizontal skew is the difference in implied volatility across ...
Related Articles
1. Investing

### What's Skewness?

Skewness describes how a data distribution leans.

### Trading with Gaussian models of statistics

The study of statistics originated from Carl Friedrich Gauss and helps us understand markets, prices and probabilities, among other applications.
3. Investing

### Optimize your portfolio using normal distribution

Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.
4. Investing

### Bet Smarter With the Monte Carlo Simulation

This technique can reduce uncertainty in estimating future outcomes.

### How to Save Clients from RMD Aggregation Mistakes

Advisors can help clients avoid required minimum distribution mistakes in their retirement plans.
6. Investing

### Bond yield curve holds predictive powers

This measure can shed light on future economic activity, inflation levels and interest rates.

Staying employed a little longer may allow for a more comfortable retirement.

### The linear regression of time and price

This investment strategy can help investors be successful by identifying price trends while eliminating human bias.
Hot Definitions
1. ### Diversification

Diversification is the strategy of investing in a variety of securities in order to lower the risk involved with putting ...
2. ### Intrinsic Value

Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
3. ### Current Assets

Current assets is a balance sheet item that represents the value of all assets that can reasonably expected to be converted ...
4. ### Volatility

Volatility measures how much the price of a security, derivative, or index fluctuates.
5. ### Money Market

The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
6. ### Cost of Debt

Cost of debt is the effective rate that a company pays on its current debt as part of its capital structure.