Revise Standard Deviation, Standard Error & Error Bars for Biology 6 (IAL) WBI16 (A2 Level) — revision notes and instant AI marking. Free to start.
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Edexcel IAL Biology • Unit 6: Practical Skills in Biology II
Standard Deviation, Standard Error & Error Bars
📊 Big idea: Two means can look different and mean nothing. Standard deviation says how spread out your data is; standard error says how much you should trust the mean itself. Error bars turn both into something you can see — and if they overlap, you have not shown a difference at all.
Summary — What This Topic Covers
What standard deviation measures, and what a large one tells you
What standard error measures, and how it differs from SD
Why increasing n shrinks the standard error but not the standard deviation
Drawing and reading error bars
Using overlap to judge whether a difference is worth testing
1. Standard Deviation
Key Term
Standard deviation (s) measures how spread out individual values are about their mean. A small s means the data is tightly clustered; a large s means it is widely scattered.
Set A: 20 21 20 22 21 mean 20.8 s ≈ 0.8 tight
Set B: 12 28 19 30 15 mean 20.8 s ≈ 7.8 scattered
IDENTICAL MEANS — completely different data.
Quoting the mean alone would hide that entirely.
In a roughly normal distribution, about 68 % of values lie within one standard deviation of the mean, and about 95 % within two. That is what makes s interpretable rather than just a number.
What it tells you biologically
A large standard deviation in a biological sample usually reflects genuine variation between individuals, not sloppy measurement. Organisms differ — that is biology, not error.
2. Standard Error
The formula
SE = s ÷ √n
where s is the standard deviation and n the number of measurements.
The distinction that matters
Standard deviation describes the spread of the data. Standard error describes the uncertainty in the mean — how far your calculated mean is likely to be from the true population mean.
s = 8.0, n = 4 SE = 8.0 ÷ √4 = 8.0 ÷ 2 = 4.00
s = 8.0, n = 16 SE = 8.0 ÷ √16 = 8.0 ÷ 4 = 2.00
s = 8.0, n = 64 SE = 8.0 ÷ √64 = 8.0 ÷ 8 = 1.00
the DATA is just as spread out in all three
but the MEAN is four times better pinned down in the last
What mark schemes look for
Increasing n reduces the standard error but does not reduce the standard deviation. The spread of the population is a fact about the organisms; only your confidence in the mean improves with more data.
3. Drawing Error Bars
Plot the mean as the point or bar height
Draw a vertical line extending one SE above and one SE below the mean — or sometimes ±2 SE, or ±1 SD
Always state what the bars show in the axis label or a key — "error bars show ± 1 standard error". Unlabelled bars are uninterpretable
Bars are drawn symmetrically about the mean
rate │ ┬
│ │ ┬
│ ● │
│ │ ● the bars overlap → the difference
│ ┴ │ between these means may be chance
│ ┴
└──────────────────────────
A B
4. Reading Overlap
The rule of thumb
If error bars overlap, the difference between the means is unlikely to be significant — it could easily be explained by random variation.
If they do not overlap, a real difference is likely, and a statistical test is worth carrying out to confirm it.
The limit of the rule
Overlap is a guide, not proof. Only a statistical test can tell you the probability that a difference arose by chance. Say "suggests" when describing error bars, and "shows" only after a test.
This is why error bars are drawn before a t-test is run: they tell you whether the test is worth doing, and they let a reader see the evidence rather than take your word for it.
5. Calculating s by Hand
You are usually given s or a calculator, but the method is examinable.
Divide by n − 1, not n, when working from a sample rather than a whole population. Using n underestimates the spread, and this is the step most often got wrong.
Practice Questions
Practice Question 1
Two sets of data have the same mean of 20.8 but standard deviations of 0.8 and 7.8. Explain what this tells you.
Practice Question 2
A student calculates a standard deviation of 6.0 from 9 measurements. Calculate the standard error and explain what it represents.
Practice Question 3
Explain why increasing the sample size reduces the standard error but not the standard deviation.
Practice Question 4
Two means are plotted with error bars showing ± 1 standard error. The bars overlap slightly. State what conclusion can be drawn and what should be done next.
What to Memorise
s = spread of the dataSE = uncertainty in the meanSE = s ÷ √nBigger n → smaller SE, same s68 % within 1 s, 95 % within 2 sAlways state what the bars showBars overlap → probably not significantOverlap suggests, a test showsDivide by n − 1 for a sample
Concepts Checklist
Exam Tips
What mark schemes look for
The SD/SE distinction stated clearly: spread of the data versus uncertainty in the mean. It is the most examined point in this topic.
The trap
Saying more repeats reduce the standard deviation. They do not — variation between organisms is real and does not shrink because you measured more of them.
Easy marks
Label the error bars. "Error bars show ± 1 standard error" is a mark, and unlabelled bars cannot be interpreted at all.
Worth remembering
Use "suggests" for error bars and "shows" only after a statistical test. Examiners notice the difference.