# Standard Normal Variate (Z) Calculator

getcalc.com's **Standard Normal Variate (Z-score) calculator** to measure how much *standard deviation*, a member X in a distribution or population deviates from its *mean* or to find what are all the well or under performing members in a group or distribution in statistical experiments. Users can also use this Z-score calculator to generate complete work to learn how to find normalized score of a member of distribution or solve grade school students's standard (Z) score worksheet problems. The below are some of the example calculations with work that generated by this normalized score calculator.

## What is Z-score & its Purpose?

**Z-score** is well known by other names as standard normal variate, standard score, normalized score or normal score is a numerical value which represents how many standard deviation a member X in a distribution or population deviates from its mean in statistical surveys or experiments. The normalized score which tells how an individual member or element X of a population close to the mean (μ) or common behavior of the distribution. The standard normal variate score generally used to identify the well and under-performing members of a population. The higher or lower normalized score represents the higher or lower deviation of a member from its population mean or central location of the data distribution respectively. The lower Z-scores of each members of population collectively improves the standard deviation of the distribution and so the uncertainty of expected results become low. Users may use this Z-score calculator to find each individual members deviation from mean of distribution which involved in the statistical surveys or experiments.

## Standard Normal Variate (Z-score) Formula

The below formula is the mathematical represenation for standard normal variate or Z-score to find the deviation of a member from its population mean or common behavior of the distribution. Find the mean and standard deviation of the distribution and apply the values in the below Z-score formula to find normalized value of a member of population.