The $z\text{-}$score, also known as the $z\text{-}$value, represents the number of standard deviations that a given value $x$ is from the mean of a data set. The following formula can be used to convert any $x\text{-}$value into its corresponding $z\text{-}$score.

Here, $\mu$ represents the mean and $\sigma$ the standard deviation of the distribution. The $z\text{-}$value corresponding to a sample mean $\bar{x}$ is called a $z\text{-}$statistic and is calculated using a similar formula.

In this formula, $s$ is the standard deviation of the sample, $n$ is the sample size, and $\mu$ is the population mean.

Example

Consider a distribution with mean $12$ and standard deviation $2.5.$ The $z\text{-}$score corresponding to $x=11.5$ is computed as follows. Consequently, $11.5$ is $0.2$ standard deviations to the left of the mean. The $z\text{-}$scores can be used to standardize a normal distribution. Then, for a random $z\text{-}$value of a standard normal distribution, the Standard Normal Table can be used to determine the corresponding area under the curve.