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

Standardizing a Score

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Now that you know the mean and standard deviation of the data set Movie Runtimes (G Rated 1990-2016) using the statistical tool above, you can calculate any observation’s [latex]z[/latex]-score to locate it in the data set relative to the mean.

It is important to note that the distance of a particular movie runtime from the mean is not measured in minutes; rather, it is measured in standard deviations.

A [latex]z[/latex]-score simply tells us how many standard deviations a given value is from the mean. Thus, a [latex]z[/latex]-score of [latex]-2.3[/latex] is an observation that is [latex]2.3[/latex] standard deviations below the mean, and a [latex]z[/latex]-score of [latex]2.3[/latex] is an observation that is [latex]2.3[/latex] standard deviations above the mean. It is important to note that [latex]z[/latex]-scores do not have units associated with them.