This Z Score calculator finds the Z score by considering a given raw score value, the mean and the standard deviation of the population to which the raw score (standardized random value) belongs. There is more info below the form.

## How does this Z Score calculator work?

This statistics tool has 2 tabs, each one being designated to a specific method to determine the Z score /standard score for a specific raw value:

- By first method you have to provide the raw score, population mean and the population standard deviation values.
- In case of the second approach on determining the Z score you have to know the raw score and the sample numbers of the population separated bysemicolon. Practically it first calculates the population mean and the population standard deviation of the given sample, then it applies the standard formula of the Z Score.

## Z Score formula

Z Score is known as the Standard Score and it represents the method of calculating how many standard deviations in a data sample is above or below the mean. The algorithm behind this Z Score calculator uses the formula explained here:

Z Score = (x- µ)/ σ

Where: x = raw score value; µ = population mean; σ = population standard deviation.

## Example of two calculations

Case 1: For a given raw score value 5.2, population mean of 3.9 and population standard deviation of 0.62 the Z score is 2.09677419.

Case 2: If the ras score is considered to be 5 and the sample size as:

1;2;3;4;5;

6;7;8;9;10;

11;12;13;14;15;

16;17;18;19;20;

21;22;23;24;25

... will result in a Z score of -1.109400.

15 Apr, 2015