Deep-Dive Guides · Data Analysis & Error
Data Analysis & Error — the complete deep dive
One guide dense enough to take you from "I can average five numbers" to CSIR-NET Part-C mastery. The organising idea: a measurement without an uncertainty is not a result.
Free extract — the opening section of the guide, in full.
0. How to use this guide — every result has an uncertainty
The single mental discipline: for any number you report, ask how sure am I, and why? Fix this map:
| Block | Central question | Tool |
|---|---|---|
| Describe | What is the central value & spread? | mean x̄, standard deviation s, RSD |
| State confidence | What range plausibly contains the true value? | confidence interval x̄ ± t·s/√n |
| Propagate | How does uncertainty flow through a calculation? | quadrature rules (add absolute; multiply relative) |
| Test | Is a difference real or just noise? | t-test, F-test, Q-test |
| Fit | What line best relates x and y, and how good is it? | least-squares regression, r/r² |
The three questions to ask of any error problem: (1) Is the error random or systematic — because statistics only tames random error; systematic error needs a different fix. (2) Am I adding/subtracting or multiplying/dividing — because that decides whether absolute or relative uncertainties combine. (3) Am I comparing to a known value, to another data set, or to a suspected outlier — because that picks the test (t vs t vs Q). Answer these and the right formula is obvious.
Read the rest of this guide
The remaining 11 sections — Types of error; accuracy vs precision, Describing data: mean, standard deviation, distribution, The normal distribution & confidence intervals, Propagation of error and more — are part of ChemVidya Full Access, along with the other guides, the books, the study notes and 6,000+ practice questions with worked solutions.