STEM MODEL AND EVIDENCE WORKBENCH
Combine repeated values with stated standard uncertainties and expose weighted mean, scatter, and reference-bias evidence.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Weight i is one divided by standard uncertainty squared. Weighted mean is the sum of weight times value divided by total weight. Internal combined uncertainty is the square root of one over total weight. Chi-square sums weighted squared residuals and reduced chi-square divides by n minus one. Reference z divides mean-minus-reference by combined uncertainty. Reduced chi-square near one suggests scatter broadly compatible with entered independent uncertainties; a large value prompts checks for under-reported uncertainty, drift, outliers, or model differences. Reference z is a bias signal only because uncertainty in the reference and shared systematic effects are omitted.
Confirm the task, approved source, units, notation, signs, model assumptions, and review threshold. Keep an unchanged copy of measurements or learner responses.
Run the worked example, inspect every intermediate row, and compare the result with a hand calculation, diagram, physical model, periodic table, or approved laboratory method.
Record the method, assumptions, uncertainty, units, classifications, and flagged rows. Verify the editable report independently before instruction, assessment, or laboratory use.
How to interpret the result
Use when repeated measurements have different stated standard uncertainties and a transparent weighted summary is needed. It does not estimate uncertainties from raw instrument records, correct calibration, detect outliers automatically, model correlated or systematic error, certify traceability, or replace the laboratory uncertainty budget and quality process.
Four fictional mass readings near 50 g have standard uncertainties from 0.03 to 0.06 g. The smallest-uncertainty trial receives the greatest weight. The report gives the weighted mean, internal combined uncertainty, standardized residuals, reduced chi-square for scatter, and difference from the 50.00 g reference in uncertainty units.
Weight i is one divided by standard uncertainty squared. Weighted mean is the sum of weight times value divided by total weight. Internal combined uncertainty is the square root of one over total weight. Chi-square sums weighted squared residuals and reduced chi-square divides by n minus one. Reference z divides mean-minus-reference by combined uncertainty.
Reduced chi-square near one suggests scatter broadly compatible with entered independent uncertainties; a large value prompts checks for under-reported uncertainty, drift, outliers, or model differences. Reference z is a bias signal only because uncertainty in the reference and shared systematic effects are omitted.
Do not use tolerances as standard uncertainties without conversion, weight by one over uncertainty instead of its square, include correlated repeats as independent, discard a high residual automatically, or report the internal uncertainty as a complete uncertainty budget. Retain raw data, calibration, resolution, and method records.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose learning, certify an experiment, identify a substance, establish a structure, or replace teacher, laboratory, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the school-approved system.
No. It describes entered evidence under one disclosed rule. Compare several evidence sources and ask for reasoning before drawing a conclusion.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow the course method and academic-integrity rules.
YOUR NIRMION
