Standard Deviation

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What is 'Standard Deviation'

Standard deviation is a measure of the dispersion of a set of data from its mean. If the data points are further from the mean, there is higher deviation within the data set. Standard deviation is calculated as the square root of variance by determining the variation between each data point relative to the mean.

BREAKING DOWN 'Standard Deviation'

In finance, standard deviation is applied to the annual rate of return of an investment to measure the investment's volatility. Standard deviation is a statistical measurement that sheds light on historical volatility. For example, a volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is lower. A large dispersion indicates how much the return on the fund is deviating from the expected normal returns.

Key Fundamental Risk Measures

Investment firms report the standard deviation of their mutual funds and other products. In the finance industry, standard deviation is one of the key fundamental risk measures that analysts, portfolio managers, wealth advisors and financial planners use. Also, because it is easy to understand, this statistic is often reported to the end clients and investors on a regular basis.

Calculating a Standard Deviation

The formula for standard deviation uses three variables. The first variable is to be the value of each point within the data set, traditionally listed as x, with a sub-number denoting each additional variable (x, x1, x2, x3, etc.). The mean, or average, of the data points is applied to the value of the variable M, and the number of data points involved is assigned to the variable n.

To determine the mean value, the values of the data points must be added together, and that total is then divided by the number of data points that were included. For example, if the data points were 5, 7, 3 and 7, the total would be 22. That total of 22 would then be divided by the number of data points, in this case 4, resulting in a mean of 5.5. This leads to the following determinations: M=5.5 and n=4.

The variance is determined by subtracting the value of the mean from each data point, resulting in -0.5, 1.5, -1.5 and 1.5 . Each of those values are then squared, resulting in 0.25, 2.25, 2.25 and 2.25. The square values are then added together, resulting in a total of 7, which is then divided by the value of n-1, which is 3 in this instance, resulting in a variance approximately of 2.33.

The square root of the variance is then calculated, resulting in the standard deviation of approximately 1.53.

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