How is the z-score defined?

The z-score is defined as the number of standard deviations a data point is from the mean of a data set. It provides a way to standardize scores on different scales, allowing for comparison across varied distributions. By converting raw scores into z-scores, it becomes easier to identify how unusual or typical a particular data point is relative to the overall distribution.

A z-score is calculated using the formula:

[ z = \frac{(X - \mu)}{\sigma} ]

where (X) is the raw score, (\mu) is the mean of the data, and (\sigma) is the standard deviation. This relationship highlights how far the score stands from the average, in units of standard deviation.

Understanding this concept is crucial for data analysis, especially when looking to interpret how specific values fall within the context of the overall data distribution.