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5.3.1Tools

Applying General Mathematics in Biology — IB Biology HL Revision Notes & Topical Questions

5 min read 5 parts Lesson 7 of 10

📚 IB Biology HL Hub / Topical Revision
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Part 1 of 5Number Skills

5.3.1 Applying General Mathematics in Biology
Decimals and fractions
  • Quantities such as cell size are often decimals or fractions,
    • and answers should be given to a sensible number of significant figures.
Ratios
  • A ratio such as 3 : 1 compares quantities, and can be used to scale up expected numbers from a cross.
Percentages
  • A percentage expresses a part as a fraction of 100, for example percentage cover in a quadrat.
Scientific notation
  • Very large or small numbers are written as a × 10ⁿ, so 0.000 002 5 m is 2.5 × 10⁻⁶ m.
Estimation
  • Rounding values before a calculation gives a quick check that the final answer is of a sensible size.

Part 2 of 5Averages, Spread and Change

Averages, Spread and Change
Mean, median and mode
  • The mean is the sum divided by the number of values, the median is the middle value and the mode is the most frequent value.
Range and quartiles
  • The range is the largest minus the smallest value, and quartiles divide ordered data into four equal parts.
Percentage change
  • Percentage change = (final − initial) ÷ initial × 100, where a negative answer shows a decrease.
Rate of change
  • Rate = change in quantity ÷ time taken, found from a graph by the gradient of a tangent for curves.
Data types
  • Discrete data are counts of separate items, whereas continuous data are measurements that can take any value within a range.
DataTypeExample
Number of leavesDiscrete6 leaves
Leaf lengthContinuous7.4 cm
Blood groupCategoricalAB

Part 3 of 5Choosing Statistical Tests

Chi-squared test
  • It compares observed and expected counts in categories, for example offspring phenotypes.
t-test
  • It compares the means of two sets of continuous data to decide if they are significantly different.
Correlation
  • The correlation coefficient measures how strongly two variables vary together, but correlation does not prove cause.
Significance
  • A probability below 0.05 means the difference is unlikely to be due to chance alone.

Part 4 of 5Worked Example

Question

  • The mass of a plant is 5.2 g at the start of an experiment and 6.5 g at the end.
  • Calculate the percentage change in mass.

  1. Change = final − initial = 6.5 − 5.2 = 1.3 g.
  2. Divide by the initial mass1.3 ÷ 5.2 = 0.25.
  3. Multiply by 100 to give a percentage: 25%.

Answer The mass increases by 25%.

Part 5 of 5Exam Checklist & Tips

5.3.1 – Key Points for the Exam

  • Mean The sum of the values divided by the number of values.
  • Percentage change The change as a percentage of the initial value.
  • Discrete data Data that can take only separate values, such as counts.
  • Continuous data Data that can take any value in a range, such as measurements.

Common Mistakes

  • Dividing by the final value instead of the initial value when finding percentage change.
  • Applying a t-test to categorical counts.
  • Treating a correlation as proof that one variable causes the other.
  • Giving answers to too many or too few significant figures.

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