While there are many different ways to measure variability within a set of data, two of the most popular are standard deviation and average deviation. Though very similar, the calculation and interpretation of these two differ in some key ways. Determining range and volatility is especially important in the finance industry, so professionals in areas such as accounting, investing and economics should be very familiar with both concepts.
Standard deviation is the most common measure of variability and is frequently used to determine the volatility of stock markets or other investments. To calculate the standard deviation, you must first determine the variance. This is done by subtracting the mean from each data point and then squaring, summing and averaging the differences. Variance in itself is an excellent measure of variability and range, as a larger variance reflects a greater spread in the underlying data. The standard deviation is simply the square root of the variance. Squaring the differences between each point and the mean avoids the issue of negative differences for values below the mean, but it means the variance is no longer in the same unit of measure as the original data. Taking the root of the variance means the standard deviation returns to the original unit of measure and is easier to interpret and utilize in further calculations.
The average deviation, also called the mean absolute deviation, is another measure of variability. However, average deviation utilizes absolute values instead of squares to circumvent the issue of negative differences between data and the mean. To calculate the average deviation, simply subtract the mean from each value, then sum and average the absolute values of the differences. The mean absolute value is used less frequently because the use of absolute values makes further calculations more complicated and unwieldy than using the simple standard deviation.

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