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 a particular observation is within a normal distribution.

5 Must Know Facts For Your Next Test

1. The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.
2. Z-scores can be positive or negative; positive indicates above the mean, while negative indicates below the mean.
3. A z-score of 0 means the data point is exactly at the mean.
4. Z-scores are essential for calculating probabilities and percentiles in a normal distribution.
5. In large samples, z-scores approximate t-scores, making them useful in hypothesis testing.

Review Questions

• What does a z-score tell you about a data point's position relative to the mean?
• How do you calculate a z-score for a given data point?
• Why are z-scores important when working with confidence intervals?

Related terms

Standard Deviation:

A measure of dispersion that indicates how spread out values are around the mean in a dataset.

Normal Distribution: A continuous probability distribution characterized by its bell-shaped curve, symmetric around its mean.

$t$-score: $t$-scores are similar to z-scores but used when sample sizes are small and population standard deviation is unknown.