A Z-score, also known as a standard score, is a statistical measurement that quantifies how far a particular data point is from the mean (average) of a dataset in terms of standard deviations. It’s a way to standardize and compare data points from different distributions. The formula for calculating the Z-score of a data point (X) in a dataset with a mean (μ) and standard deviation (σ) is:
The Z-score tells you how many standard deviations a data point is away from the mean. It can be positive or negative, depending on whether the data point is above or below the mean, respectively.
The interpretation of Z-scores is as follows:
• A Z-score of 0 indicates that the data point is exactly at the mean.
• A positive Z-score means the data point is above the mean.
• A negative Z-score means the data point is below the mean.
• The magnitude of the Z-score tells you how far away from the mean the data point is in terms of standard deviations.
Z-scores are commonly used in statistics for various purposes, such as identifying outliers, comparing data from different distributions, and making standardized comparisons in fields like finance, education, and healthcare. They are also used in hypothesis testing and constructing confidence intervals.