Combining Repeated and Instrument Uncertainty
When repeated observations and instrument resolution both matter, the stated uncertainty must use the experiment's prescribed rule and cannot be smaller than the defensible resolution contribution; statistical and bounded uncertainties must not be mixed silently.
Why this shows up in the exam
Repeated sensor measurements · Timing trials · Metrology reports
Learn the idea
A complete elementary result respects both observed spread and the instrument's finite resolution. Repeated readings may cluster more tightly than the scale can resolve, so the final uncertainty cannot honestly imply more discrimination than the instrument provides.
🧠 Memory hook: Averaging reduces random scatter, not the ruler's physical ticks or a fixed bias.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- reported Delta x >= resolution contribution — resolution places a floor on defensible uncertainty
- standard error scales as s/sqrt(n) — statistical mean uncertainty when that model is explicitly applicable
How to approach it
- 1Identify the required uncertainty convention
- 2Compute repeatability spread
- 3Compare with resolution and report the defensible limit
Common slip-ups that cost marks
- •Claiming unlimited precision from many repeats
- •Mixing mean absolute error and standard error without stating a model
- •Ignoring instrument resolution
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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