api: "YAML JSON TOON Database"
version: "1.0.0"
format: "json"
dataset:
  slug: "statistics-basics"
  title: "Statistics Basics"
  description: "Fundamental statistical measures and concepts."
  category: "Mathematics"
  category_slug: "mathematics"
  tags: "math,statistics,probability,data-science"
  view_count: 0
data:
  - measure: "Mean (Average)"
    description: "Sum of all values divided by count."
    formula: "xbar = Sum(xi) / n"
  - measure: "Median"
    description: "Middle value when data is sorted. Robust to outliers."
    formula: "Middle element (or avg of two)"
  - measure: "Mode"
    description: "Most frequently occurring value in the dataset."
    formula: "argmax frequency"
  - measure: "Variance"
    description: "Average squared deviation from the mean."
    formula: "sigma2 = Sum(xi - xbar)2 / n"
  - measure: "Standard Deviation"
    description: "Square root of variance; measures spread in original units."
    formula: "sigma = sqrt(variance)"
  - measure: "Correlation"
    description: "Measure of linear relationship between two variables."
    formula: "r = Cov(X,Y) / (sigma_x * sigma_y)"
  - measure: "Z-Score"
    description: "Number of standard deviations a value is from the mean."
    formula: "z = (x - xbar) / sigma"