What is the 'Empirical Rule'
The empirical rule is the statistical rule stating that for a normal distribution, almost all data will fall within three standard deviations of the mean. Broken down, the empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.
BREAKING DOWN 'Empirical Rule'
The empirical rule is often referred to as the threesigma rule or the 689599.7 rule. The Empirical Rule is most often used in statistics for forecasting final outcomes. After a standard deviation is calculated, and before exact data can be collected, this rule can be used as a rough estimate as to the outcome of the impending data. This probability can be used in the meantime as gathering appropriate data may be time consuming, or even impossible to obtain. The empirical rule is also used as a rough way to test a distribution's "normality". If too many data points fall outside the three standard deviation boundaries, this could suggest that the distribution is not normal.Empirical Rule Examples
Imagine a population of animals in a zoo is known to be normally distributed. The average animal lives to be 13.1 years old and the standard deviation of lifespans is 1.5 years. If someone wants to know the probability that an animal will live longer than 14.6 years, they could use the empirical rule. Knowing the distribution's mean is 13.1 years old, the following age ranges occur for each standard deviation:
One standard deviation: (13.1  1.5) to (13.1 + 1.5), or 11.6 to 14.6
Two standard deviations: (13.1  2 x 1.5) to (13.1 + 2 x 1.5), or 10.1 to 16.1
Three standard deviations: (13.1  3 x 1.5) to (13.1 + 3 x 1.5), or, 8.6 to 17.6
The person solving this problem needs to calculate the total probability of the animal living 14.6 years or long. The empirical rule shows that 68% of the distribution lies within one standard deviation, in this case, from 11.6 to 14.6 years. Thus, the remaining 32% of the distribution lies outside this range. Half lies above 14.6 and half lies below 11.6. So the probability of the animal living more than 14.6 is 16% (32% divided by two).
As another example, assume instead that the average animal in the zoo lives to 10 years of age, with a standard deviation of 1.4 years. Assume the zookeeper is attempting to figure out the probability of an animal living more than 7.2 years. This distribution looks as follows:
One standard deviation: 8.6 to 11.4 years
Two standard deviations: 7.2 to 12.8 years
Three standard deviations: 5.8 to 14.2 years
The empirical rule states that 95% of the distribution lies within two standard deviations. Thus, 5% lies outside of two standard deviations; half above 12.8 years and half below 7.2 years. Thus, the probability of living more than 7.2 years is:
95% + (5% / 2) = 97.5%

Standard Deviation
A measure of the dispersion of a set of data from its mean, calculated ... 
Bell Curve
A bell curve is the most common type of distribution for a variable. 
T Distribution
A T distribution is a type of probability function that is appropriate ... 
Tail Risk
A form of portfolio risk that arises when the possibility that ... 
Empirical Probability
A form of probability that is based on some event occurring, ... 
Risk Management
Risk management occurs anytime an investor or fund manager analyzes ...

Investing
Why Standard Deviation Should Matter to Investors
Think of standard deviation as a thermometer for risk, or better yet, anxiety. 
Investing
A Simplified Approach To Calculating Volatility
Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it: the historical method. 
Investing
Using Normal Distribution Formula To Optimize Your Portfolio
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
Investing
Are Your ETFs Too Risky? Learn How to Evaluate Them
Learn how to identify ETFs with greater risk and volatility. See why some investors include higher volatility ETFs in pursuit of greater returns. 
Investing
Calculating Tracking Error
Tracking error is the difference between the return on a portfolio or fund, and the benchmark it is expected to mirror (or track). 
Investing
Multivariate Models: The Monte Carlo Analysis
This decisionmaking tool integrates the idea that every decision has an impact on overall risk. 
Investing
5 Ways To Measure Mutual Fund Risk
These statistical measurements highlight how to mitigate risk and increase rewards. 
Investing
Understanding Volatility Measurements
How do you choose a fund with an optimal riskreward combination? We teach you about standard deviation, beta and more! 
Investing
What are the 5 US Equity Funds For Steady Returns?
Discover five highly rated mutual funds that have long histories, are stable, and have marketbeating returns. All of these funds have longtenured managers. 
Investing
Find The Right Fit With Probability Distributions
Discover a few of the most popular probability distributions and how to calculate them.

What is standard deviation used for in mutual funds?
See how standard deviation is helpful in evaluating a mutual fund's performance. Use it in combination with other measurements ... Read Answer >> 
What is the difference between the expected return and the standard deviation of ...
Learn about the expected return and standard deviation and the difference between the expected return and standard deviation ... Read Answer >> 
What is a relative standard error?
Find out how to distinguish between mean, standard deviation, standard error and relative standard error in statistical survey ... Read Answer >> 
What is the difference between standard deviation and variance?
Understand the difference between standard deviation and variance; learn how each is calculated and how these concepts are ... Read Answer >> 
What metrics should I use to evaluate the risk return tradeoff for a mutual fund?
Understand the key metrics used to analyze mutual funds and how investors can use each measurement to determine the riskreward ... Read Answer >>