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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 
\[ s_{f}=\frac{1}{n} (|x_{1f}-m_{f}|+|x_{2f}-m_{f}|+...+|x_{nf}-m_{f}|) \]

Speaker notes:

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