Standard Deviation vs. Variance: An Overview
Standard deviation and variance may be basic mathematical concepts, but they play important roles throughout the financial sector, including the areas of accounting, economics, and investing. In the latter, for example, a firm grasp of the calculation and interpretation of these two measurements is crucial for the creation of an effective trading strategy.
Both standard deviation and variance are derived from the mean of a given data set. If the mean is simply the average of all data points, the variance measures the average degree to which each point differs from the mean. The greater the variance, the larger the overall data range.
Standard deviation is a statistic that looks at how far from the mean a group of numbers is, by using the square root of the variance. The calculation of variance uses squares because it weights outliers more heavily than data very near the mean. This also prevents differences above the mean from canceling out those below, which can sometimes result in a variance of zero.
Standard deviation is calculated as the square root of variance by figuring out the variation between each data point relative to the mean. If the points are further from the mean, there is a higher deviation within the date; if they are closer to the mean, there is a lower deviation. So the more spread out the group of numbers, the higher the standard deviation.
To calculate standard deviation, add up all the data points and divide by the number of data points, calculate the variance for each data point and then find the square root of the variance.
The variance is the average of the squared differences from the mean. To ascertain the variance, first calculate the difference between each point and the mean; then, square and average the results.
For example, say a data set consists of the numbers between 1 and 10, giving a mean of 5.5. Squaring the difference between each data point and the mean yields a sum of squares of 82.5. The variance is calculated by subtracting this sum from the mean and then dividing by N (the number of values)-1. This thus results in a variance of roughly 9.17. If the standard deviation is the square root of the variance, in this example, it would be about 3.03.
However, because of this squaring, the variance is no longer in the same unit of measurement as the original data. Taking the root of the variance means the standard deviation is restored to the original unit of measure and therefore much easier to measure.
For traders and analysts, these two concepts are of paramount importance as the standard deviation is used to measure security and market volatility, which in turn plays a large role in creating a profitable trade strategy.
Standard deviation is one of the key methods that analysts, portfolio managers, and advisors use to determine risk. The wider the standard deviation, or range, the greater the risk. Securities that are close to their means are seen as less risky, as they are more likely to continue behaving as such. Securities with large trading ranges that tend to spike or change direction are riskier. Risk is not a bad thing, however, as the riskier the security, the greater potential for payout as well as loss.
- Standard deviation looks at how spread out a group of numbers is from the mean, by looking at the square root of the variance.
- The variance measures the average degree to which each point differs from the mean—the average of all data points.
- The two concepts are useful and significant to traders, who use them to measure market volatility.