Z-scores

Definition

A z-score measures how many standard deviations a data point is from the mean of a distribution. It is calculated using the formula $z = \frac{(X - \mu)}{\sigma}$ where $X$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

5 Must Know Facts For Your Next Test

1. A z-score indicates whether a data point is above or below the mean and by how many standard deviations.
2. Positive z-scores indicate values above the mean, while negative z-scores indicate values below the mean.
3. The standard normal distribution has a mean of 0 and a standard deviation of 1.
4. Z-scores are used to compare different data points from different normal distributions.
5. In a normal distribution, approximately 68% of the data lies within one standard deviation (z-score between -1 and 1) from the mean.

Review Questions

• What does a z-score tell you about a data point in relation to its distribution?
• How do you calculate a z-score?
• What percentage of data in a normal distribution falls within one standard deviation of the mean?

Related terms

Standard Deviation:

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

Normal Distribution: A probability distribution that is symmetric about its mean, showing that data near the mean are more frequent in occurrence.

Percentile:

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