Z-Score

A z-score puts different values on a common scale, making it easy to see how unusual a value is. It is calculated by subtracting the mean from the value and dividing the result by the standard deviation.

For example, if an investment's average annual return is 8% with a standard deviation of 4%, a return of 16% has a z-score of 2, meaning it is two standard deviations above average. A return of 4% has a z-score of minus 1.

A z-score of 0 means the value equals the mean. Positive z-scores are above the mean, and negative ones are below it. For data that follow a normal distribution, about 68% of values have z-scores between minus 1 and 1, and about 95% fall between minus 2 and 2. A z-score beyond 3 or minus 3 is very unusual.

Z-scores are used to identify outliers, compare values from different data sets and standardise data for analysis. In finance, a well-known application is the Altman Z-score, which combines several financial ratios into a single number to estimate the likelihood that a company will go bankrupt, although it is a different calculation from the statistical z-score.