# Standard Deviation

the annual rate of return of an investment, to measure the investment's volatility, or "risk".
Standard deviation in investment
standard deviation
statistical measure of the degree to which an individual value in a probability distribution tends to vary from the mean of the distribution. It is widely applied in modern portfolio theory , for example, where the past performance of securities is used to determine the range of possible future performances and a probability is attached to each performance. Mutual fund analysts average the returns over three years, then determine the range in which returns have varied from that mean. So, if the mean return is 10% and the range has been +25% to -5%, standard deviation is 15.
Standard deviation in business terms
standard deviation
statistical measure of the degree to which an individual value in a probability distribution tends to vary from the mean of the distribution. From a normal distribution, one standard deviation includes about 66% of the population; two standard deviations include about 95%.

When you say that an investment like a stock market index fund has an expected return of 9%, you're saying that in any year there is a chance that your return will be better than 9% and a chance that it will be worse. To get more specific about your chances, you need to specify the expected volatility of the investment, as well as its expected return.
The volatility of an investment is given by the statistical measure known as the standard deviation of the return rate.
a standard deviation of zero would mean an investment has a return rate that never varies, like a bank account paying compound interest at a guaranteed rate.
The Standard Deviation Formula

Simple Example of Calculating Standard Deviation
Let's say we wanted to calculate the standard deviation for the amounts of gold coins pirates on a pirate ship have.
There are 100 pirates on the ship. In statistical terms this means we have a population of...