*Z Score Calculator* is an online statistics tool for data analysis programmed to compare the relative standings of items from distributions with different means and/or different standard deviations. This calculator generate the Z score value according to the given inputs of data set random value, sample mean and standard deviation

### Definition

**Z Score** also known as Standard Score, is the method of calculating how many standard deviations in a data set is above or below the mean. The distance between the mean and a given Z score in every normal distribution cuts off a fixed ratio of the total area below the curve. Z scores are particularly informative when the distribution to which they refer is normal. The standard score transformation is useful in particular when seeking to compare the relative standings of items from distributions with different means and; or with different standard deviations

### Z Score Formula

The Standard Score can be calculated from the following formula

where

**x** is a raw score to be standardized

**μ** is the mean of the population

**σ** is the standard deviation of the population

The raw score is below the mean when z is negative. Similarly the raw score is above the mean when z is positive. The quantity represented by standard score z is the distance between the raw score and the population mean in terms of standard deviation

The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand theory of Probability and Statistics. The set of ideas which is intended to offer the way for making scientific implication from such resulting summarized data. In many applications it is necessary to calculate the Standard Score for a given set of data. With this online standard score calculator you can effortlessly make your z score calculation for given data set