# What is a Standard Deviation?

Definition: Standard Deviation (SD) is a statistical measure that captures the difference between the average and the outliers in a set of data. In other words, standard deviation measures how volatile a set of data is.

## What Does Standard Deviation Mean?

What is the definition of standard deviation? Standard Deviation is a statistical tool that is used widely by statisticians, economists, financial investors, mathematicians, and government officials. It allows these experts to see how variable a collection of data is. Furthermore, SD is calculated as the square root of the variance of the data. Specifically in finance, investors can use SD to determine the volatility of a certain portfolio of investments.

Let’s look at an example.

## Example

Matthew has just graduated, and has entered the financial industry as an investment analyst for a large firm. One of his first tasks is to determine the SD of a portfolio of three investments: AAC, BBA, and CCD. These investments have annualized returns of 8%, 15%, and 13%, respectively. First, Matthew knows he must calculate the mean, or average, of the data: (.08 + .15 + .13) x 100 / (3) = 12%.

Furthermore, he knows that the variance is simply the difference between each investment’s return, and the mean. Thus, the variance for AAC is (8% – 12%) = -4%, the variance for BBA is (15% – 12%) = 3%, and the variance for CCD is (13% – 12%) = 1%. Then, he squares these values to arrive at .16%, .09%, and .01%.

Lastly, he adds these values together, and arrives at 0.26%, which is divided by 2 to arrive at the total variance of 0.13%. Then, he takes the square root of the total variance, or .0013,. which equals a deviation of 3.6%. Although this formula can seem intimidating, it is actually an extremely useful tool for investors and non-investors to use to find patterns and information in a set of data.

## Summary Definition

Standard Deviations: Standard deviation means a statistical measurement used to calculate the significance of items as they relate to averages, means, and outliers.

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