Z-Score and Standard Deviation: An Overview
Although the finance industry can be complex, an understanding of the calculation and interpretation of basic mathematical building blocks is still the foundation for success, whether in accounting, economics or investing. Standard deviation and Z-score are two such fundamentals. A firm grasp of how to calculate and utilize these two measurements enables a more thorough analysis of patterns and changes in any data set, from business expenditures to stock prices.
The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. To calculate Z-score, simply subtract the mean from each data point and divide the result by the standard deviation. For data points that are below the mean, the Z-score is negative. In most large data sets, 99% of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above and below the mean.
Z-scores offer analysts a way to compare data against a norm. A given company’s financial information is more meaningful when you know how it compares to that of other, comparable companies. A Z-score of zero indicates that the data point being analyzed is exactly average, situated among the norm. A Z-score of 1 indicates that the data is one standard deviation from the mean, while a Z-score of -1 places the data one standard deviation below the mean. The higher the Z-score, the further from the norm the data can be considered the be.
Standard deviation is essentially a reflection of the amount of variability within a given data set. It shows the extent to which the individual data points in a data set vary from the mean. A large standard deviation means that more of your data points deviate from the norm. A small standard deviation means that more of your data points are clustered near the norm. Standard deviation can be visualized as a bell curve, with a flatter, more spread-out bell curve representing a large standard deviation and a steep, tall bell curve representing a small standard deviation.
To calculate standard deviation, first, calculate the difference between each data point and the mean. The differences are then squared, summed and averaged to produce the variance. The standard deviation is simply the square root of the variance, which brings it back to the original unit of measure.
In investing, standard deviation and Z-score can be useful tools in determining market volatility. As the standard deviation increases, it indicates that price action varies widely within the established time frame. Given this information, the Z-score of a particular price indicates how typical or atypical this movement is based on previous performance.
Bollinger Bands are a technical indicator used by traders and analysts to assess market volatility based on standard deviation. Simply put, they are a visual representation of the Z-score. For any given price, the number of standard deviations from the mean is reflected by the number of Bollinger Bands between the price and the exponential moving average (EMA).
- The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.
- Standard deviation is essentially a reflection of the amount of variability within a given data set.
- Bollinger Bands are a technical indicator used by traders and analysts to assess market volatility based on standard deviation.