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Z-Score

Standard Score (Z-Score)

The number of standard deviations a data point lies from the mean, used to compare values across different distributions.

技术细节

Descriptive z-score summarize datasets: mean (average, sensitive to outliers), median (middle value, robust to outliers), and mode (most frequent). Standard deviation measures dispersion — in a normal distribution, 68% of values fall within ±1σ, 95% within ±2σ, and 99.7% within ±3σ. For skewed distributions (income, website traffic), median is more representative than mean. The coefficient of variation (σ/μ) normalizes dispersion for comparing datasets with different scales.

示例

```
Dataset: [3, 7, 7, 2, 9, 1, 6]

  Mean:     (3+7+7+2+9+1+6) / 7 = 5.0
  Median:   Sort → [1,2,3,6,7,7,9] → 6 (middle value)
  Mode:     7 (most frequent)
  Std Dev:  σ ≈ 2.83
  Variance: σ² = 8.0
```

Categories

Z-Score

技术细节

示例

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