Standardizing vs Z-Score

Standardizing rescales a value so it reports distance from the mean in standard deviations rather than in the original units, which lets you compare scores measured on different scales. The formula is $z = \frac{x - \mu}{\sigma}$ for a population, where $\mu$ (mu) is the mean and $\sigma$ (sigma) is the standard deviation, and $z = \frac{x - \bar{x}}{s}$ for a sample. A time of 73 seconds drawn from a distribution with mean 65 seconds and standard deviation 4 seconds standardizes to $z = (73 - 65)/4 = 2$, so it is 2 standard deviations above the mean. Standardizing shifts and rescales the values but leaves the shape alone, so a skewed distribution is still skewed afterward.

A z-score standardizes a value by measuring its distance from the mean in standard deviations. You compute it as $z = \frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ (mu) is the mean, and $\sigma$ (sigma) is the standard deviation. For example, a score of 85 in a distribution with mean 70 and standard deviation 5 has $z = (85 - 70)/5 = 3$, so it sits 3 standard deviations above the mean. A negative z-score means the value is below the mean.