Module 11: Background You’ll Need 1

  • Calculate and interpret [latex]z[/latex]-scores.

[latex]z[/latex]-scores

A [latex]z[/latex]-score or standardized score measures a value’s distance from the mean in units of standard deviation. A positive [latex]z[/latex]-score indicates the value is above the mean, whereas a negative [latex]z[/latex]-score indicates the value is below the mean.

[latex]z=\dfrac{\text{value}-\text{mean}}{\text{standard deviation}}[/latex]

A [latex]z[/latex]-score of a value is calculated by subtracting the mean and then dividing by the standard deviation. Similarly, we can calculate the [latex]z[/latex]-score of a sample mean by:

[latex]z=\dfrac{\bar{x}-[\text{mean of } \bar{x}'s]}{\text{std. deviation of } \bar{x}'s}[/latex] [latex]= \dfrac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/latex]