Z-score

Definition

A z-score represents the number of standard deviations a data point is from the mean. It is used to determine how unusual or typical a value is within a normal distribution.

5 Must Know Facts For Your Next Test

1. Z-scores are calculated using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.
2. In business statistics, z-scores can be used to understand confidence intervals when dealing with normally distributed data.
3. When the population standard deviation is unknown and sample size is small (usually n < 30), t-scores are often used instead of z-scores.
4. A z-score of 0 indicates that the data point is exactly at the mean.
5. Positive z-scores indicate values above the mean, while negative z-scores indicate values below 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 if you know the mean and standard deviation?
• Why might t-scores be preferred over z-scores in certain statistical analyses?

Related terms

Confidence Interval: A range of values derived from sample statistics that likely contains the true population parameter.

t-Score: Used instead of z-scores when sample sizes are small and/or population standard deviation is unknown; calculated based on sample data.

Standard Deviation: A measure of dispersion in a dataset, indicating how spread out numbers are around the mean.