Practice Z-Score (Standard Score) in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The number of standard deviations a value is from the mean: z = \frac{x - \mu}{\sigma}.

Z-scores put everything on the same scale. A z-score of +2 means 'two standard deviations above average' - unusually high. A z-score of -1 means 'one SD below average' - somewhat low but normal.

Example 1

medium
A student scores 78 on a test where \mu = 70 and \sigma = 4. Calculate her z-score and interpret it.

Example 2

hard
Alice scores 85 in Maths (\mu = 75, \sigma = 5) and 90 in English (\mu = 80, \sigma = 10). In which subject did she perform better relative to her class?

Example 3

medium
A data value has a z-score of -1.5. If the distribution has \mu = 50 and \sigma = 8, find the original value.

Example 4

medium
In a class, test scores have mean \mu = 65 and standard deviation \sigma = 5. A student scores 55. Find the z-score and interpret it.
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