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Mathematical Proof & Formula

Arithmetic Mean Grade Formula

Finds the unweighted average score across multiple tests or class assignments.

Mathematically Verified Proof
•Standard Curricular Mathematics•Peer-Reviewed Formulas
\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i

Variable Definitions

Variable SymbolMathematical Meaning
x_iIndividual test score i
nTotal number of tests taken

Calculation Steps

  1. Add all individual test scores together.
  2. Divide by the total number of test scores.

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Authoritative References & Academic Standards

Vetted against official government, institutional, and collegiate guidelines

.org sourceOfficial Source
Arithmetic Mean and Weighted Averages Overview
Khan Academy Mathematics

Educational mathematical foundations for calculating arithmetic means, category weights, and statistical dispersion.

.org sourceOfficial Source
Weighted Arithmetic Mean Mathematics
Wikipedia (Mathematical Foundations)

Formal mathematical formulation of weighted linear averages and convex combinations in multi-factor scoring systems.

.org sourceOfficial Source
Assessment Standards for School Mathematics
National Council of Teachers of Mathematics (NCTM)

National research guidelines on rubric construction, formative grading, and equitable student achievement evaluation.