The Central Limit Theorem states that the the distribution of \bar{X} approaches normality as n increases, regardless of what the distribution of X is.
Stated more formally, for samples of size n drawn from a distribution with mean \mu and finite variance \sigma^2, the distribution of the sample mean is approximately N\left(\mu, \frac{\sigma^2}{n} \right) for sufficiently large n.
Stated more formally, for samples of size n drawn from a distribution with mean \mu and finite variance \sigma^2, the distribution of the sample mean is approximately N\left(\mu, \frac{\sigma^2}{n} \right) for sufficiently large n.
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This question appears in the following syllabi:
Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|
AQA A-Level (UK - Pre-2017) | S1 | Estimation | Central Limit Theorem | - |
AQA A2 Further Maths 2017 | Statistics | Central Limit Theorem - Extra | Central Limit Theorem | - |
AQA AS/A2 Further Maths 2017 | Statistics | Central Limit Theorem - Extra | Central Limit Theorem | - |
CCEA A-Level (NI) | S2 | Estimation | Central Limit Theorem | - |
CIE A-Level (UK) | S2 | Estimation | Central Limit Theorem | - |
Edexcel A-Level (UK - Pre-2017) | S3 | Estimation | Central Limit Theorem | - |
Edexcel A2 Further Maths 2017 | Further Statistics 1 | Central Limit Theorem | Central Limit Theorem | - |
Edexcel AS/A2 Further Maths 2017 | Further Statistics 1 | Central Limit Theorem | Central Limit Theorem | - |
I.B. Higher Level | 7 | Estimation | Central Limit Theorem | - |
Methods (UK) | M15 | Estimation | Central Limit Theorem | - |
OCR A-Level (UK - Pre-2017) | S2 | Estimation | Central Limit Theorem | - |
OCR A2 Further Maths 2017 | Statistics | Hypothesis Tests and Confidence Intervals | Central Limit Theorem | - |
OCR MEI A2 Further Maths 2017 | Statistics B | Sample Mean and Central Limit Theorem | Central Limit Theorem | - |
OCR-MEI A-Level (UK - Pre-2017) | S3 | Estimation | Central Limit Theorem | - |
Universal (all site questions) | E | Estimation | Central Limit Theorem | - |
WJEC A-Level (Wales) | S2 | Estimation | Central Limit Theorem | - |