##### Statistical Analysis with R For Dummies
The R function for calculating standard scores is called `scale()`. Supply a vector of scores, and `scale()` returns a vector of z-scores along with, helpfully, the mean and the standard deviation.

To show `scale()` in action, isolate a subset of the `Cars93` data frame. (It's in the MASS package. On the Packages tab, check the box next to MASS if it's unchecked.)

Specifically, create a vector of the horsepowers of 8-cylinder cars from the USA:

`> Horsepower.USA.Eight <- Cars93\$Horsepower[Origin == "USA" & Cylinders == 8]`

```> Horsepower.USA.Eight ``` `[1] 200 295 170 300 190 210`

And now for the z-scores:

```> scale(Horsepower.USA.Eight) ``` ```[,1] ``` ```[1,] -0.4925263 ``` ```[2,] 1.2089283 ``` ```[3,] -1.0298278 ``` ```[4,] 1.2984785 ``` ```[5,] -0.6716268 ``` ```[6,] -0.3134259 ``` ```attr(,"scaled:center") ``` ```[1] 227.5 ``` ```attr(,"scaled:scale") ``` ```[1] 55.83458 ``` That last value is s, not Σ. If you have to base your z-scores on Σ, divide each element in the vector by the square root of (N-1)/N:

```> N <- length(Horsepower.USA.Eight) ``` ```> scale(Horsepower.USA.Eight)/sqrt((N-1)/N) ``` ```[,1] ``` `[1,] -0.5395356`

```[2,] 1.3243146 ``` ```[3,] -1.1281198 ``` ```[4,] 1.4224120 ``` ```[5,] -0.7357303 ``` ```[6,] -0.3433408 ``` ```attr(,"scaled:center") ``` ```[1] 227.5 ``` ```attr(,"scaled:scale") ``` `[1] 55.83458`

Notice that `scale() `still returns s.