## What is a Z-score?

The Z-score, or standard score, is a fractional representation of standard deviations from the mean value. Accordingly, z-scores often have a distribution with no average and standard deviation of 1. Formally, the z-score is defined as:

## How does a Z-score work?

As described above, the z-score works by taking a sample score and subtracting the mean score, before then dividing by the standard deviation of the total population. It can be easy to think of this using an example. Imagine having a score of 70 out of 100, where the mean score is 60, and the standard deviation is 15. Using the z-score function, one can calculate the z-score of .6667 from the data. By comparing the z-score the standard normal distribution table, one can determine that the probability of a score being greater than .67 is .2514 or 25.14%. In short, the score is better than roughly 75% of the rest of the scores.