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, also called the mean absolute deviation. Though similar, the calculation and interpretation of these two measurements 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

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. To do this, you must find the mean, or average, of the data points by adding them up and dividing the total by the number of data points. Then, subtract the mean from each data point and square each one. Finally, find the average of each of those squared differences. The standard deviation is simply the square root of the resulting variance.

Variance in itself is an excellent measure of variability and range, as a larger variance reflects a greater spread in the underlying data. 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 square root of the variance means the standard deviation returns to the original unit of measure and is easier to interpret and use in further calculations.

Average Deviation, or Mean Absolute Deviation

The average deviation, or mean absolute deviation, is another measure of variability. It is calculated similarly to standard deviation, but it uses absolute values instead of squares to circumvent the issue of negative differences between the data points and their mean. To calculate the average deviation, simply subtract the mean of all of the data points from each data point value. Next, add and average the absolute values of the differences.

Use of Average and Standard Deviation

Standard deviation is often used in creating strategies for investing and trading because it can help measure market volatility and predict performance trends. For example, an index fund should have a low average deviation when compared to its benchmark fund. That means it's closely tracking the benchmark, as it's supposed to do. More aggressive funds may have a higher

The mean absolute deviationĀ is used less frequently because the use of absolute values makes further calculations more complicated and unwieldy than using the simple standard deviation.