Library › Biology 6 (IAL) WBI16 › Standard Deviation, Standard Error & Error Bars

A2 Level · Biology 6 (IAL) WBI16

Standard Deviation, Standard Error & Error Bars

Revise Standard Deviation, Standard Error & Error Bars for Biology 6 (IAL) WBI16 (A2 Level) — revision notes, 2 practice questions and instant AI marking.

📖 Revision notes · preview

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.

Practice Questions

🔓 Read the full Standard Deviation, Standard Error & Error Bars note → You're seeing the preview · sign in to read it all

Also in the full note

What to Memorise
Concepts Checklist
Exam Tips
5. Calculating s by Hand

What's inside

📖 Revision notes ◉ 2 practice questions 🎯 Learn mode ✦ AI flashcards ✓ Instant AI marking 🧊 3D explorers 🧪 Experiments & simulations 📈 Progress tracking