Z-Score Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

A student scored

82

on an exam where the mean was

74

and the standard deviation was

8

. What is the student's z-score?

1
Recall the z-score formula: $z = \frac{x - \mu}{\sigma}$ , which measures how many standard deviations $x$ is from the mean.
2
Identify given values: $x = 82$ , $\mu = 74$ , $\sigma = 8$ .
3
Substitute and calculate: $z = \frac{82 - 74}{8} = \frac{8}{8} = 1.0$

Answer

z = 1.0

A z-score of

1.0

means the student scored exactly one standard deviation above the mean. Z-scores allow comparison across different scales.

About Z-Score

A z-score measures how many standard deviations a data value is above or below the mean: $z = (x - \mu)/\sigma$ .

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