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Replicates · microscopy · data interpretation

Averages, spread and mitotic index

Calculate means, medians, ranges and mitotic index. Interpret supplied standard deviations, with sample standard-deviation calculation in OCR mode.

Method and worked examples ↓

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Check your answer after each question. Use a calculator where needed.

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How to approach these questions

  1. Include every valid measurement when calculating a mean. Do not discard a value merely because it is inconvenient.
  2. Order values before finding a median. For an even number of values, average the two middle values.
  3. Compare spread as well as means. A smaller supplied standard deviation indicates readings clustered more closely around their mean.
  4. For percentage mitotic index, multiply the fraction of cells in mitosis by 100.
  5. OCR sample-standard-deviation practice uses s = √[Σ(x − mean)²/(n − 1)]. AQA mode practises interpretation of supplied standard deviations, not that calculation.

Worked examples

Five seedlings are 8, 10, 12, 14 and 16 mm tall. Calculate mean height and range.

Mean = 60 ÷ 5 = 12 mm. Range = 16 − 8 = 8 mm. Both retain the height unit; the mean describes the centre and the range describes the observed extremes.

Of 240 observed root-tip cells, 36 are in mitosis. Calculate the mitotic index as a percentage.

Mitotic index = 36 ÷ 240 × 100 = 15%. This is the proportion of observed cells in mitosis. Using it to estimate the proportion of time spent in mitosis needs assumptions about growth, sampling and cell-cycle states.

Two seedling groups have the same mean height, 12 mm. Group A has heights 11, 12 and 13 mm; group B has 8, 12 and 16 mm. Compare their spread. In OCR mode, also calculate their sample standard deviations.

Ranges are 2 mm for A and 8 mm for B, so B has more observed spread. For sample standard deviation, divide the sum of squared deviations by n − 1. A: √[(1 + 0 + 1)/2] = 1 mm. B: √[(16 + 0 + 16)/2] = 4 mm. These three-value examples illustrate spread; they do not establish a population difference or statistical significance. AQA practice here interprets supplied standard deviations; the calculation extension is for OCR.

Keep practising

Topic map and study list · Practical data guides · Active recall decks

Course resources

AQA A-level Biology · OCR A A-level Biology · Textbook answers

Skill coverage follows the common A-level science subject content. Check your board’s current requirements: AQA 7402 and OCR A H420.