Statistics & graphs · SL/HL
SD & standard error
Find sample SD, population SD and standard error.
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Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Result & working
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Spread of individual values around the mean. | |
| Uncertainty in the estimated mean due to sampling variability. |
Worked example
- Data
- 4.8, 5.1, 4.9, 5.2, 5.0
sample SD = 0.1581139
Follow the example steps
- mean = 5
- Σ(x−x̄)² = 0.1
- sample SD = √[0.1/(5−1)] = 0.1581139
- SE = SD/√n = 0.1581139/√5 = 0.07071068
Common mistakes
Standard deviation and standard error describe different things.
Incorrect approach
For 2, 4, 6: sample SD = 2/√3
Correct approach
Sample SD = 2; SEM = 2/√3 ≈ 1.155
More checks before you submit
- Do not report error bars without saying what they show.
Method notes
State whether error bars represent SD, SE or another quantity; these are not interchangeable.