Statistics Formulas​

These are fundamental statistics formulas that are crucial for basic statistical analysis:
Descriptive Statistics
  1. Mean (Average): µ = Σx / N (for population), x̄ = Σx / n (for sample)
  2. Median: Middle value in an ordered data set
  3. Mode: Most frequent value in a data set
  4. Range: Max(x) - Min(x)
  5. Variance: σ² = Σ[(x - µ)²] / N (for population), s² = Σ[(x - x̄)²] / (n - 1) (for sample)
  6. Standard Deviation: σ = √σ² (for population), s = √s² (for sample)
Probability Distribution
  1. Probability of an Event: P(E) = Number of favorable outcomes / Total outcomes
  2. Complement Rule: P(E') = 1 - P(E)
  3. Addition Rule: P(E or F) = P(E) + P(F) - P(E and F)
  4. Multiplication Rule: P(E and F) = P(E) * P(F|E)
Binomial Distribution
  1. Binomial Coefficient (Combinations): C(n, k) = n! / [k!(n-k)!]
  2. Binomial Probability: P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Normal Distribution
  1. Standard Normal Distribution: Z = (X - µ) / σ
  2. Empirical Rule: ~68% of data within 1σ, ~95% within 2σ, ~99.7% within 3σ
Hypothesis Testing
  1. Z-score for Hypothesis Test: Z = (x̄ - µ₀) / (σ / √n)
  2. T-score for Hypothesis Test: T = (x̄ - µ₀) / (s / √n)
Confidence Intervals
  1. Confidence Interval (Z-distribution): CI = x̄ ± Z * (σ/√n)
  2. Confidence Interval (T-distribution): CI = x̄ ± T * (s/√n)
Correlation and Regression
  1. Pearson's Correlation Coefficient: r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)² * Σ(yi - ȳ)²]
  2. Slope of Regression Line: b = r * (Sy / Sx)
  3. Y-Intercept of Regression Line: a = ȳ - b*x̄
ANOVA (Analysis of Variance)
  1. Total Sum of Squares: SST = Σ(yi - ȳ)²
  2. Between-group Sum of Squares: SSB = Σn*(ȳ - ȳ)²
  3. Within-group Sum of Squares: SSW = Σ(yi - ȳ)²
  4. F-statistic: F = (SSB / dfb) / (SSW / dfw)
While this list does cover many common statistics formulas, it's crucial to remember that the application of these formulas varies greatly depending on the specific situation and data set at hand. Also, advanced statistics topics like multivariate analysis, time series, stochastic processes, etc., require more complex and numerous formulas.