Z-Score and the Empirical Rule: Learn It 2

  • Calculate z-scores to explain the location of data points.
  • Compare observations using z-scores and the Empirical Rule.

Standardize Value ([latex]z[/latex]-score)

So far, you have calculated values that were a given number of standard deviations above and below the mean. You discovered when you divided the difference between the value and the mean by the standard deviation, that the result was a positive number of standard deviations (for values above the mean) or a negative number of standard deviations (for values below the mean). That is, a resulting negative can be thought of as indicating a value that lies to the left of the mean, and the positive indicates a value that lies to the right of the mean.