Standard deviation and variance, though basic mathematical concepts, play important roles in many areas of the financial sector, including accounting, economics and investing. In investing, for example, a firm grasp of the calculation and interpretation of these two measurements is crucial for the creation of an effective trade strategy.
Both standard deviation and variance are derived from the mean of a given data set. Whereas 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. For the variance, first calculate the difference between each point and the mean. The results are squared and averaged to produce the variance. For simplicity’s sake, this example uses a data set consisting of the numbers between 1 and 10, giving a mean of 5.5. Squaring the difference between each data point and the mean and averaging the squares renders a variance of 8.25.
Standard deviation is simply 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. 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. For traders and analysts, these two concepts are of paramount importance as the standard deviation is used to measure market volatility, which in turn plays a large role in creating a profitable trade strategy.