3.4 - Implementation and measurements
- Syllabus
- 2021
- Topic
- 3.4
- Level
- AS
Learning objectives
3.4.1Number of readingsEvaluate the number of readings taken.3.4.2Range of measurementsEvaluate the range of measurements taken.3.4.3Significant figuresEvaluate the significant figures used.3.4.4Inconsistent readingsCheck a reading inconsistent with other readings and record instrument readings using the correct number of significant figures.3.4.5Improving experimental methodExplain how an experimental method may be improved, including using additional apparatus to reduce errors.
Judge whether there are enough readings for the intended conclusion
The number of readings must support the analysis. Count both the distinct settings of the independent variable and the repeat readings at each setting: they answer different questions.
| Reading choice | What it allows | Sign that the data are too weak |
|---|---|---|
| distinct settings | reveal a trend and support a best-fit line or curve | only a few points, so one value can dominate the apparent pattern |
| repeats at one setting | reveal scatter, identify a suspect value and support a mean | a single value gives no evidence of reproducibility |
Judge sufficiency from the purpose and the data shown. A graph needs enough well-distributed points to distinguish a relationship from scatter. A quantity affected by reaction time or judgement usually needs repeats. State the missing evidence and its consequence, rather than demanding an unexplained fixed total.
Taking more different settings does not replace repeats, and repeating one setting does not create a useful graph. 'Five is always enough' is not a rule: the pattern, spread and experimental constraints determine whether the number is defensible.
A useful measurement range tests the relationship beyond a narrow window
Range is the span from the smallest to the largest value measured. A useful range is wide enough for the predicted change in the dependent variable to stand out from uncertainty and to test whether the relationship continues across the accessible domain.
| Check | Stronger data choice |
|---|---|
| endpoints | extend safely towards lower and higher feasible values |
| distribution | place settings across the whole span, not in one cluster |
| predicted behaviour | include values where competing trends or curvature would separate |
| instrument limits | stay within calibrated range and readable resolution |
If every temperature lies between 29.5∘C and 50.0∘C, a prediction about a broader temperature dependence may remain untested. Measurements below or above that interval would strengthen the test if they are safe and measurable.
Range is not the same as the number of readings or the spacing between them. Many closely packed values can still cover a poor range, while two distant endpoints alone do not provide enough points to establish a trend.
Recorded precision must follow the measurement, not cosmetic zeros
Record a direct reading to the precision justified by the instrument. Repeated readings of the same quantity with the same instrument should normally use consistent decimal places, because the final digit represents the same scale interval or display resolution each time.
| Feature | Meaning | Practical check |
|---|---|---|
| decimal places | digits after the decimal point | do equal-resolution raw readings use the same place value? |
| significant figures | meaningful digits from the first non-zero digit | is a calculated result rounded to precision supported by its inputs? |
| unit | scale attached to the value | is the heading or each value labelled consistently? |
Keep extra digits during a calculation, then round once at the end. A result calculated from measurements quoted to 3 significant figures should not be reported with a long calculator display; an appropriate final value is usually 3 significant figures unless a stated uncertainty gives a stronger rule.
Consistency does not mean forcing every column to the same decimal places. Different quantities and instruments can justify different precision. Trailing zeros are meaningful only when they communicate measured resolution, not when they are added to make a table look uniform.
Check a suspect reading before deciding whether to discard it
A reading is suspect when it conflicts with repeats, a clear trend or the physical sequence of the data. First check transcription, units, instrument interpretation and any calculation; repeat the measurement where possible before deciding how to use it.
| Evidence | Defensible response |
|---|---|
| obvious recording or calculation error | correct it only from recoverable raw evidence |
| repeated value remains far outside the experimental scatter | label it anomalous and justify exclusion from a mean or fit |
| difference is comparable with ordinary scatter | retain it; there is no evidence that it is invalid |
| no check is possible | show it transparently and discuss its effect on the conclusion |
For an analogue scale or micrometer diagram, identify the smallest division, read the main scale and any secondary scale in the correct order, apply a known zero correction, attach the unit and record only justified digits. This prevents a misread instrument from masquerading as anomalous physics.
Do not discard a value merely because it weakens the expected relationship, and do not average it away without inspection. A defensible decision compares the deviation with the spread or trend and records the reason.
Improve the cause of error, then examine the trade-off
A useful improvement names the weak measurement, identifies the error mechanism, changes the method or apparatus, and explains why the change reduces that error. 'Use better equipment' is incomplete without this causal link.
| Weakness | Targeted improvement | Why it helps | Limitation to check |
|---|---|---|---|
| manual start/stop timing | two light gates with an electronic timer or data logger | removes most reaction-time variation | gate positions and triggering edges must match the intended interval |
| event difficult to judge | video viewed frame by frame | makes the start/end criterion reviewable | frame rate limits time resolution |
| ruler not perpendicular to motion | set square and fixed fiducial marker | controls alignment and reference position | marker thickness still affects judgement |
| percentage timing uncertainty large | increase the measured interval or slow the motion safely | the same absolute timing uncertainty is a smaller fraction | changed conditions must not alter the relationship being tested |
Evaluate advantages and disadvantages in the actual setup. Extra apparatus can reduce one uncertainty while introducing alignment, calibration, triggering or setup errors. Prefer the modification that addresses the dominant limitation without changing the variable being investigated.
More apparatus is not automatically an improvement, and repeating unchanged biased measurements does not remove systematic error. The explanation must connect cause, modification and expected effect.