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A2 · A2 3 Practical Skills in A2 Biology

Standard deviation and error bars in A-level Biology

The short answer

Standard deviation measures how spread out data are around the mean. A small standard deviation means the repeats cluster tightly and the mean is reliable; a large one means the data are variable. Roughly 68% of values lie within one standard deviation of the mean.

Calculating it

  • Find the mean of your repeats.
  • Subtract the mean from each value and square each difference.
  • Add the squares and divide by (n − 1).
  • Take the square root. Quote it in the same units as the original measurements.

Standard deviation vs standard error

Standard deviation describes the spread of the data themselves. Standard error (standard deviation ÷ √n) describes how precisely the sample mean estimates the true population mean, and it gets smaller as you take more repeats. Error bars on a graph can show either — always say which, and say which you used and why.

Interpreting error bars

  • Error bars that do not overlap suggest a real difference between the means and justify a statistical test.
  • Overlapping error bars suggest any difference may be due to chance — never claim a significant difference from overlap alone.
  • Long error bars indicate variable data, so more repeats are needed before drawing a firm conclusion.
  • State clearly that error bars show variability, not error in the sense of mistakes.

Phrases that earn the marks

  • standard deviation measures the spread of data about the mean
  • a smaller standard deviation means more reliable / less variable data
  • error bars overlap, so the difference may not be significant
  • a statistical test is needed to confirm significance
  • standard error decreases as sample size increases

Where marks get lost

  • Confusing standard deviation with the range.
  • Concluding a significant difference from non-overlapping bars without a test.
  • Dividing by n instead of (n − 1) for a sample.
  • Omitting units from the quoted value.

Try these standard deviation biology a level questions yourself

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AS 3 / A2 3 practical skills — interpreting spread · 3 marks

Two samples of leaves had the same mean length but sample A had a standard deviation of 1.2 mm and sample B a standard deviation of 6.4 mm. Explain what this tells you about the two samples.

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These questions are written in the style of the CCEA GCE Biology (2016) papers and are not reproduced from any live paper. CCEA owns the copyright in its question papers and mark schemes — always download the official paper and mark scheme from CCEA and use these worked answers alongside them. BioCCEA is an independent study tool and is not endorsed by CCEA.

Exam questions on standard deviation biology a level, marked

Two A2-standard questions in CCEA paper style, each with the full mark scheme, a full-mark answer written the way you should write it, and the point where most candidates drop marks.

AS 3 / A2 3 practical skills — interpreting spread · 3 marks

Two samples of leaves had the same mean length but sample A had a standard deviation of 1.2 mm and sample B a standard deviation of 6.4 mm. Explain what this tells you about the two samples.

Command word: Explain — how to answer it

Mark scheme — 3 creditworthy points

  • Standard deviation measures the spread of the data about the mean
  • Sample A has a smaller standard deviation, so its values are more closely clustered around the mean / less variable
  • Sample B is more variable / has greater dispersion, so its mean is a less reliable summary of the sample

Full-mark answer

Standard deviation measures how spread out the data are about the mean. Sample A has a much smaller standard deviation (1.2 mm), so its leaf lengths are closely clustered around the mean and there is little variation within the sample. Sample B has a standard deviation of 6.4 mm, so its values are widely dispersed and the mean is a less reliable representation of a typical leaf in that sample.

Examiner insight: 'Sample A is more accurate' scores nothing — spread is about variability, not accuracy. Use the figures given; unquoted comparisons lose the second mark.

A2 3 evaluation question · 3 marks

Error bars showing ±1 standard deviation for two treatments overlap considerably. State what conclusion can be drawn and what further analysis should be carried out.

Command word: Complete / Draw / Plot / Label — how to answer it

Mark scheme — 3 creditworthy points

  • Overlapping error bars suggest the difference between the means is not significant / may be due to chance
  • No firm conclusion can be drawn from the error bars alone
  • A statistical test (t-test) should be carried out to determine whether the difference is significant at p = 0.05

Full-mark answer

Because the error bars overlap considerably, the difference between the two means is unlikely to be significant and may be due to chance, so no firm conclusion can be drawn from the graph alone. A t-test should be carried out to compare the two means and the calculated value compared with the critical value at p = 0.05 to determine whether the difference is statistically significant.

Examiner insight: Naming the specific test and the p = 0.05 threshold is the third mark. 'Do more repeats' is not creditworthy here.

These questions are written in the style of the CCEA GCE Biology (2016) papers and are not reproduced from any live paper. CCEA owns the copyright in its question papers and mark schemes — always download the official paper and mark scheme from CCEA and use these worked answers alongside them. BioCCEA is an independent study tool and is not endorsed by CCEA.

Download the official CCEA paper and mark scheme

Common questions

What does a large standard deviation tell you?
That the individual results are widely spread around the mean, so the mean is a less reliable summary and more repeats are needed.
Should error bars show standard deviation or standard error?
Either is acceptable at A-level as long as you label which you used. Standard error is more useful when comparing means.
Do overlapping error bars mean there is no difference?
No — they mean any difference may be due to chance. Only a statistical test can settle it.

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