{
    "api": "YAML JSON TOON Database",
    "version": "1.0.0",
    "format": "json",
    "dataset": {
        "id": 2906,
        "slug": "statistics-basics",
        "title": "Statistics Basics",
        "description": "Fundamental statistical measures and concepts.",
        "summary": "The basic measures of central tendency, spread and association: mean, median, mode, variance, standard deviation, correlation and the z-score, plus range, interquartile range, covariance, skewness, standard error, coefficient of variation, confidence intervals and the p-value, each with its formula.",
        "use_when": [
            "You need the definition and formula for a descriptive statistic.",
            "You are choosing a summary that is robust to outliers."
        ],
        "caveats": [
            "Sample and population versions differ (n versus n - 1 in the denominator).",
            "A p-value is not the probability that a hypothesis is true, and correlation does not establish causation."
        ],
        "related": [
            "combinatorics-fundamentals",
            "ml-evaluation-metrics",
            "set-theory-basics"
        ],
        "entry_count": 15,
        "fields": [
            {
                "section": "data",
                "field": "measure",
                "type": "string",
                "example": "Mean (Average)"
            },
            {
                "section": "data",
                "field": "description",
                "type": "string",
                "example": "Sum of all values divided by count."
            },
            {
                "section": "data",
                "field": "formula",
                "type": "string",
                "example": "xbar = Sum(xi) \/ n"
            }
        ],
        "category": "Mathematics",
        "category_slug": "mathematics",
        "tags": "math,statistics,probability,data-science",
        "view_count": 35,
        "created_at": 1793403093,
        "updated_at": 1793403093
    },
    "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"
        },
        {
            "measure": "Range",
            "description": "Difference between the largest and smallest value; very sensitive to outliers.",
            "formula": "max - min"
        },
        {
            "measure": "Interquartile Range",
            "description": "Spread of the middle half of the data; robust to outliers.",
            "formula": "Q3 - Q1"
        },
        {
            "measure": "Covariance",
            "description": "How two variables vary together; positive when they tend to move in the same direction.",
            "formula": "cov(X, Y) = E[(X - mean(X)) (Y - mean(Y))]"
        },
        {
            "measure": "Skewness",
            "description": "Asymmetry of a distribution; positive when the right tail is longer.",
            "formula": "E[((X - mean) \/ sd)^3]"
        },
        {
            "measure": "Standard Error of the Mean",
            "description": "Standard deviation of the sample mean across repeated samples.",
            "formula": "sd \/ sqrt(n)"
        },
        {
            "measure": "Coefficient of Variation",
            "description": "Standard deviation relative to the mean, allowing comparison across different scales.",
            "formula": "sd \/ mean"
        },
        {
            "measure": "Confidence Interval for a Mean",
            "description": "A range computed so that, over repeated samples, it contains the true mean a stated share of the time.",
            "formula": "mean +\/- z * sd \/ sqrt(n)"
        },
        {
            "measure": "p-value",
            "description": "Probability of data at least as extreme as observed if the null hypothesis were true.",
            "formula": "P(data at least this extreme | H0)"
        }
    ]
}