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5.3.3Tools

Processing Uncertainties in Biology — IB Biology HL Revision Notes & Topical Questions

5 min read 5 parts Lesson 9 of 10

📚 IB Biology HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Part 1 of 5Types of Error

Random 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
  • 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
  • Precision Closeness of repeated measurements to each other, which is affected by random error.
Accuracy
  • Accuracy Closeness of a measurement to the true value, which is reduced by systematic error.
TypeEffect on resultsReduce by
RandomScatter around true valueRepeats, larger sample
SystematicAll values shiftedCalibration, better method

Part 2 of 5Quantifying Uncertainty

Quantifying Uncertainty
Absolute uncertainty
  • Absolute uncertainty The ± value of a measurement in the same unit as the quantity, such as ±0.5 cm³.
Percentage uncertainty
  • Percentage uncertainty Absolute uncertainty divided by the measured value, × 100.
Range
  • Range The difference between highest and lowest repeat values gives a simple idea of spread.
Standard deviation
  • Standard deviation A measure of how far the data are from the mean, and a smaller value shows less variation.
Error bars
  • 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.

  1. Volume used = 24.0 − 18.5 = 5.5 cm³.
  2. For a subtraction, add the absolute uncertainties: 0.5 + 0.5 = 1.0 cm³.
  3. 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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