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Standardizing Numeric Data
- Z-score:
\[ z=\frac{x-\mu}{\sigma } \]
- X: raw score to be standardized, μ: mean of the population, σ: standard deviation
- the distance between the raw score and the population mean in units of the standard deviation
- negative when the raw score is below the mean, “+” when above
- An alternative way: Calculate the mean absolute deviation, where
\[ m_{f}= \frac{1}{n}(x_{1f}+x_{2f}+...+x_{nf}) \]
- standardized measure (z-score):
\[ z_{if}=\frac{(x_{if}-m_{f})}{S_{f}} \]
- Using mean absolute deviation is more robust than using standard deviation
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