api: YAML JSON TOON Database
version: 1.0.0
format: json
dataset:
  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[2]: You need the definition and formula for a descriptive statistic.,You are choosing a summary that is robust to outliers.
  caveats[2]: 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[3]: combinatorics-fundamentals,ml-evaluation-metrics,set-theory-basics
  category: Mathematics
  category_slug: mathematics
  tags: "math,statistics,probability,data-science"
  view_count: 0
  entry_count: 15
  fields[3]{section,field,type,example}:
    data,measure,string,Mean (Average)
    data,description,string,Sum of all values divided by count.
    data,formula,string,xbar = Sum(xi) / n
data[15]{measure,description,formula}:
  Mean (Average),Sum of all values divided by count.,xbar = Sum(xi) / n
  Median,Middle value when data is sorted. Robust to outliers.,Middle element (or avg of two)
  Mode,Most frequently occurring value in the dataset.,argmax frequency
  Variance,Average squared deviation from the mean.,sigma2 = Sum(xi - xbar)2 / n
  Standard Deviation,Square root of variance; measures spread in original units.,sigma = sqrt(variance)
  Correlation,Measure of linear relationship between two variables.,"r = Cov(X,Y) / (sigma_x * sigma_y)"
  Z-Score,Number of standard deviations a value is from the mean.,z = (x - xbar) / sigma
  Range,Difference between the largest and smallest value; very sensitive to outliers.,max - min
  Interquartile Range,Spread of the middle half of the data; robust to outliers.,Q3 - Q1
  Covariance,How two variables vary together; positive when they tend to move in the same direction.,"cov(X, Y) = E[(X - mean(X)) (Y - mean(Y))]"
  Skewness,Asymmetry of a distribution; positive when the right tail is longer.,"E[((X - mean) / sd)^3]"
  Standard Error of the Mean,Standard deviation of the sample mean across repeated samples.,sd / sqrt(n)
  Coefficient of Variation,"Standard deviation relative to the mean, allowing comparison across different scales.",sd / mean
  Confidence Interval for a Mean,"A range computed so that, over repeated samples, it contains the true mean a stated share of the time.",mean +/- z * sd / sqrt(n)
  p-value,Probability of data at least as extreme as observed if the null hypothesis were true.,P(data at least this extreme | H0)