What Z-Score Meaning, Applications & Example
Statistical measure of a value's relationship to the mean.
What is Z-Score?
The Z-Score is a statistical measure that describes how many standard deviations a data point is from the mean of the dataset. It is used to identify outliers, normalize data, and understand the relative position of a value within a distribution. A Z-score of 0 indicates that the value is exactly at the mean, while a Z-score of 1 means the value is one standard deviation above the mean.
Z-Score Formula
\[ Z = \frac{{X - \mu}}{{\sigma}} \]Where:
- \(X\) = data point
- \(\mu\) = mean of the data
- \(\sigma\) = standard deviation of the data
Applications of Z-Score
- Outlier Detection: Identifying data points that are significantly different from the rest of the data.
- Normalization: Transforming data to a standard normal distribution for machine learning algorithms.
- Statistical Analysis: Comparing values across different datasets or populations with different units.
Example of Z-Score Calculation
If a student’s test score is 85, the class average is 80, and the standard deviation is 5, the Z-score would be:
\[ Z = \frac{{85 - 80}}{{5}} = 1 \]This means the student’s score is 1 standard deviation above the class average.