How z-Values Are Used in Statistics

By Deborah J. Rumsey

If a statistical data set has a normal distribution, it is customary to standardize all the data to obtain standard scores known as z-values or z-scores. The distribution of z-values takes on a standard normal distribution (or Z-distribution). The standard normal distribution is a special normal distribution with a mean equal to 0 and a standard deviation equal to 1.

The standard normal distribution is useful for examining the data and determining statistics like percentiles, or the percentage of the data falling between two values. So if researchers determine that the data have a normal distribution, they usually first standardize the data (by converting each data point into a z-value) and then use the standard normal distribution to explore and discuss the data in more detail.