5.3.3Tools
Processing Uncertainties in Biology — IB Biology HL Revision Notes & Topical Questions
5 min read 5 parts Lesson 9 of 10
Part 1 of 5Types of Error
Random error
- Unpredictable variation that scatters results about the true value, caused by reading judgement or natural variation,
- and reduced by repeating and averaging.
Systematic error
- A consistent shift of all results in one direction, caused by faulty equipment or method, that repeating the experiment does not remove.
Precision
- Closeness of repeated measurements to each other, which is affected by random error.
Accuracy
- Closeness of a measurement to the true value, which is reduced by systematic error.
| Type | Effect on results | Reduce by |
|---|---|---|
| Random | Scatter around true value | Repeats, larger sample |
| Systematic | All values shifted | Calibration, better method |
Part 2 of 5Quantifying Uncertainty
Quantifying Uncertainty
Absolute uncertainty
- The ± value of a measurement in the same unit as the quantity, such as ±0.5 cm³.
Percentage uncertainty
- Absolute uncertainty divided by the measured value, × 100.
Range
- The difference between highest and lowest repeat values gives a simple idea of spread.
Standard deviation
- A measure of how far the data are from the mean, and a smaller value shows less variation.
Error bars
- Bars on a graph show the range or standard deviation, and overlapping bars suggest no real difference.
Part 3 of 5Combining Uncertainties
1
When values are added or subtracted, add their absolute uncertainties.
2
When values are multiplied or divided, add their percentage uncertainties.
3
Convert the final percentage back to an absolute uncertainty if needed by multiplying by the result.
4
Round the uncertainty to one significant figure and match the decimal places of the result to the uncertainty.
5
Compare the uncertainty with the size of the change measured to judge whether a result is meaningful.
Part 4 of 5Worked Example
Question
- The volume in a burette falls from 24.0 ± 0.5 cm³ to 18.5 ± 0.5 cm³.
- Find the volume used with its absolute and percentage uncertainty.
- Volume used = 24.0 − 18.5 = 5.5 cm³.
- For a subtraction, add the absolute uncertainties: 0.5 + 0.5 = 1.0 cm³.
- Percentage uncertainty = 1.0 ÷ 5.5 × 100 = 18.2%.
Answer Volume used is 5.5 ± 1.0 cm³, a percentage uncertainty of about 18%.
Part 5 of 5Exam Checklist & Tips
5.3.3 – Key Points for the Exam
- Random error Unpredictable variation in measurements.
- Systematic error A consistent bias in the same direction in all measurements.
- Absolute uncertainty The ± value of a measurement, in its own unit.
- Standard deviation A measure of the spread of data around the mean.
Common Mistakes
- Believing that taking more repeats removes a systematic error.
- Subtracting uncertainties instead of adding them when two readings are subtracted.
- Confusing precision with accuracy.
- Quoting an uncertainty with more significant figures than the measurement itself.
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