Z-scores

Definition

A z-score measures how many standard deviations an element is from the mean of a distribution. It is calculated using the formula $z = \frac{x - \mu}{\sigma}$ where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

5 Must Know Facts For Your Next Test

1. Z-scores are used to standardize scores from different distributions for comparison.
2. A z-score of 0 indicates that the value is exactly at the mean.
3. Positive z-scores indicate values above the mean, while negative z-scores indicate values below the mean.
4. In a standard normal distribution, approximately 68% of data falls within one standard deviation (z-score between -1 and 1).
5. Z-scores can be used to find probabilities and percentiles in a normal distribution.

Review Questions

• What does a z-score represent in terms of standard deviations?
• How do you calculate a z-score for a given value in a dataset?
• What does it indicate when a z-score is negative?

Related terms

Standard Normal Distribution:

A normal distribution with a mean of 0 and a standard deviation of 1.

Percentile:

A measure indicating the value below which a given percentage of observations fall.

Standard Deviation:

A measure of the amount of variation or dispersion in a set of values.