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# Statistics

## Z-Scores

While the Boxplot and interquartile range measures position with the median. Another method is to measure position in relation to the mean using z-scores.

 The sample z-score for a measurement x is $z=\frac{x-\bar{x}}{s}$ The population z-score for a measurement x is $z=\frac{x-\mu}{\sigma}$

Example: Suppose a sample of 2000 high school seniors' verbal SAT scores is selected. The mean and standard deviation are $$\bar{x}=550,\,s=75$$. A student scored 475. What is his sample z-score?

Solution:

$z=\frac{x-\bar{x}}{s}=\frac{475-550}{75} = -1.0$

This means that the student scored 1.0 standard deviations below the sample mean.