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Normalization & z-score

⭐ Z‑Score

A z‑score tells you how many standard deviations an observation is from the mean.

z = \frac{x - \mu}{\sigma}

What it does

  • Centers the data at 0
  • Scales it so the standard deviation is 1
  • Keeps the shape of the distribution
  • Makes different datasets comparable

Example

Population mean \mu = 50 , standard deviation \sigma = 10 .
What is the z‑score of x = 65 ?

z = \frac{65 - 50}{10} = 1.5

Interpretation:
The value is 1.5 standard deviations above the mean.

🎨 Intuition


Z‑scores are like saying, “How unusual is this photo compared to the rest?”


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See also  Bernoulli distribution

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