Skip to main content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

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. 

chat loading...