What is a Z-Score?
A Z-score (also known as a Standard Score) tells you exactly how many Standard Deviations a specific number is above or below the Mean (average). It is the ultimate mathematical equalizer, allowing you to compare two completely different things fairly.
For example, if you score a 1250 on the SAT and a 26 on the ACT, which score is actually better? Because the tests use completely different grading scales, you can't compare the raw numbers. However, by converting both into Z-Scores, you can easily see which test you performed better on compared to the rest of the population.
How to Read a Z-Score
Z = 0
A Z-score of exactly zero means the raw score is identical to the population mean. You are exactly average (the 50th percentile).
Positive Z-Score
A positive number (e.g., +1.5) means the score is above the average. In standard intelligence tests, a Z-score of +2.0 puts you in the top 2% of the population.
Negative Z-Score
A negative number (e.g., -1.0) means the score is below the average. Almost all data in a normal distribution falls between -3.0 and +3.0.
The Empirical Rule (68-95-99.7)
When dealing with a normal distribution (a standard Bell Curve), Z-scores follow a very predictable and famous rule:
- 68% of all data falls between a Z-score of -1 and +1.
- 95% of all data falls between a Z-score of -2 and +2.
- 99.7% of all data falls between a Z-score of -3 and +3. If you have a Z-score beyond 3, it is considered a significant outlier!