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The Mathematical Symbols used in Statistics [email protected] [ updated: Saturday, April 19, 2008 ] “All wisdom is rooted in learning to call things by the right name.” ---Confucious (c. 500 B.C.) Purpose: The purpose of this document is clearly identify the many mathematical symbols used in typical statistics problems. Mathematics is the language of science. Statistics is the language of research. Students need to master these symbols because these symbols are the standard nomenclature in statistical reasoning. In general, Greek letters are used for measures of the population (called “parameters”) and Latin letters are used for measures of one or more samples (called “statistics”). The pronunciation and vernacular for each symbol is included as well. Symbol Concept Number of Observations (size) Mean Variance Standard Deviation Proportion Correlation Coefficient Population N (big “en”) Sample n (little “en”) μ (“mu”) σ (lower case “sigma” squared) σ (lower case “sigma”) π (lower case “pi”) ρ (lower case “rho”) x (“x-bar”) s (“ess-squared”) s (“ess”) p (little “pea”) r (little “are”) 2 2 Other Greek and Latin letters are used to symbolize various numerical quantities and mathematical transformations. Concept Summation Sum Product Type I Error Type II Error Regression – y-intercept (constant) Regression – slope Regression – actual y value Regression – predicated y value Square of the correlation (multiple) Coefficient of Determination Page 1 of 1 Symbol ∑ (upper case “sigma”) Π (upper case “pi”) α (lower case “alpha”) β (lower case “beta”) b0 b1 y (“why”) ŷ (“why hat”) r2 (little “are squared”) R2 (big “are squared”)