# Z-scores review

## What are z-scores?

A z-score measures exactly how many standard deviations above or below the mean a data point is.

Here's the formula for calculating a z-score:

Here's the same formula written with symbols:

Here are some important facts about z-scores:

- A positive z-score says the data point is above average.
- A negative z-score says the data point is below average.
- A z-score close to says the data point is close to average.
- A data point can be considered unusual if its z-score is above or below .

*Want to learn more about z-scores? Check out this video.*

### Example 1

The grades on a history midterm at Almond have a mean of and a standard deviation of .

Michael scored on the exam.

**Find the z-score for Michael's exam grade.**

Michael's z-score is . His grade was half of a standard deviation above the mean.

### Example 2

The grades on a geometry midterm at Almond have a mean of and a standard deviation of .

Michael scored on the exam.

**Find the z-score for Michael's exam grade.**

Michael's z-score is . His grade was two standard deviations below the mean.

### Practice problems

*Want to practice more problems like these? Check out this exercise.*