# Statistics - Z Score (Zero Mean) or Standard Score

## 1 - About

Any raw score from any scale can be converted to Z scores (Z scale)

In statistics, the standard score is the signed number of standard deviations by which an observation or data is above the mean.

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## 3 - Formula

$\text{Z Score} = \frac{\displaystyle \href{raw score}{X} – \href{mean}{\bar{X}}}{\href{standard_deviation}{\displaystyle \text{Standard Deviation}}}$

where:

• $\href{raw score}{X}$ is a score on an original scale (raw score)
• $\href{mean}{\bar{X}}$ is the mean

With this formula:

• The mean Z-score is Z = 0
• Positive Z scores are above average
• Negative Z scores are below average

## 4 - Percentile

Z-scores can be used to find percentile rank (Raw score ~ Z-score ~ Percentile rank)

If the distribution is normal, Z=0 means a Median percentile (50th, 50 percent of the distribution falls below the mean)

## 5 - Documentation / Reference

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data_mining/z_score.txt · Last modified: 2017/09/13 16:04 by gerardnico