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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Formula
<math> \text{Z Score} = \frac{\displaystyle \href{raw score}{X} – \href{mean}{\bar{X}}}{\href{standard_deviation}{\displaystyle \text{Standard Deviation}}} </math>
where:
- <math>\href{raw score}{X}</math> is a score on an original scale (raw score)
- <math>\href{mean}{\bar{X}}</math> 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)