Z score

Z-score or standard score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.

Definition

The Z-score is a measure of how many standard deviations an element is from the mean. It is calculated by subtracting the population mean from an individual raw score, then dividing the difference by the population standard deviation. The Z-score formula for a sample is:

Z = (X – μ) / σ

Where: Z is the Z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.

Uses

Z-scores are primarily used in Standard Normal Distribution and other statistical calculations. They are also used in the fields of Economics, Psychology, Business, and Health Sciences to compare different sets of data. In Finance, Z-scores are used in the Altman Z-score calculation to predict corporate defaults.

Advantages and Disadvantages

The main advantage of Z-scores is that they provide a direct measure of how far a data point is from the mean, and they also allow for comparison of data points from different data sets. The main disadvantage is that if the population mean or standard deviation are unknown, you cannot compute the Z-score.

See also

• Standard Deviation
• Mean
• Altman Z-score
• Standard Normal Distribution