MathLiveCentral limit theorem
For independent, identically distributed samples with finite variance, the standardized sample mean converges in distribution to a standard normal as the sample size grows. It justifies using normal approximations for sample means and sums in statistics.
\frac{\bar{X}_n-\mu}{\sigma/\sqrt{n}}\xrightarrow{d}N(0,1)What the symbols mean
| sample mean of n independent observations | |
| population mean of each observation | |
| population standard deviation of each observation | |
| sample size | |
| standard normal distribution |
About this formula
- FieldStatistics
- TopicProbability theory
- LevelUniversity
- Also calledCLT, sample mean approaches normal distribution, standardized sample mean convergence to normal, sum of independent random variables normal limit, large sample normal approximation, Lindeberg-Levy theorem
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