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

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.

## 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

## 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)

## Documentation / Reference

Discover More
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Statistics - Z Scale

The Z-scale is the standard scale in statistics where: the standard deviation is 1 unit. and the mean is zero Any score from any scale can be converted to Z scores
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(Normalize|Standardize) is a scale transformation on a numeric variable distribution to have: zero as mean (See Z score) the max and the min of the distribution into a given numeric range (normally...