What is the purpose of a Z-score?

The primary purpose of a Z-score is to represent the number of standard deviations a data point is from the mean of its dataset. By calculating a Z-score, you can gauge how far away a particular value lies from the average, allowing for the standardization of scores across different datasets or scales. This helps in understanding how unusual or typical a particular observation is relative to the rest of the data.

A Z-score can also facilitate comparisons between different datasets, as it transforms the data into a common scale based on the mean and standard deviation. For example, a Z-score of +2 indicates that the value is two standard deviations above the mean, while a Z-score of -1 indicates one standard deviation below the mean. This powerful concept is essential in statistical analysis, hypothesis testing, and identifying outliers within data.

Understanding Z-scores aids analysts in making inferences about how a specific observation stands in the context of the overall distribution. It is an invaluable tool in business statistics for various applications, including quality control and performance assessment.