wunder beta📘 How to use a z-score
A z-score locates a value relative to its mean in standard-deviation units. The same scale can compare a test score, a wait time, or a plant height even when the raw units differ.
What you’ll learn
- Locate a z-scoreDefine a z-score and calculate it from a value, mean, and standard deviation.A z-score locates an observation in standard deviation units relative to its distribution.
- Interpret the scoreInterpret direction, magnitude, cross-scale comparison, and the limits of probability claims.The sign and size describe location; comparing z-scores requires sensible reference groups and a separate model for areas.
- Tables and conclusionsUse a normal reference table when appropriate and report a z-score with its original value and limits.Normal-table areas depend on model fit; a sound conclusion keeps the raw measurement visible.
Questions this course answers
What does a z-score measure?
A z-score expresses how far an observation is from the mean after scaling by the standard deviation.
What is the z-score for x = 74 when the mean is 68 and the standard deviation is 4?
Subtract the mean and divide by the standard deviation: (74 - 68) / 4 = 1.5.
What does a negative z-score indicate?
The sign gives direction relative to the mean; a negative score is below it.
When should you use a normal table after calculating a z-score?
Normal-table probabilities rely on an appropriate normal model and careful interpretation of the table format.
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