Z-Score

Z-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.

Calculation

The Z-Score is calculated using the following formula:

Z = (X - μ) / σ

Where:

• Z is the Z-Score,
• X is the value of the individual data point,
• μ is the mean of the population, and
• σ is the standard deviation of the population.

Uses

Z-Scores are used in various fields, including psychology, health sciences, business and finance. They are used to compare different data points from different data sets, and can be used to analyze trends and patterns.

In medicine, Z-Scores are used to measure the relative health of a patient. For example, in cardiology, Z-Scores are used to predict the likelihood of heart disease. In psychology, Z-Scores are used to measure the relative severity of a patient's symptoms.

Advantages and Disadvantages

The main advantage of using Z-Scores is that they are easy to calculate and understand. They allow for easy comparison of data points from different data sets.

However, Z-Scores are not always the best choice for data analysis. They can be misleading if the data is not normally distributed, or if there are outliers in the data.

See Also

• Standard deviation
• Mean
• Statistics

References

• How to Calculate a Z-Score – Statistics How To
• Z-Scores Review – Khan Academy