Standardizing

Standardizing converts a value to a z-score by subtracting the mean and dividing by the standard deviation.

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=xμσz = \frac{x - \mu}{\sigma} for a population, where μ\mu (mu) is the mean and σ\sigma (sigma) is the standard deviation, and z=xxˉsz = \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=(7365)/4=2z = (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.

Where this comes up

More describing data terms, or browse the full statistics glossary.