Stage 2 · Lesson 4 of 8
Samples, the CLT and standard error
You almost never see the whole , only a . If you took many samples, each would give a slightly different average; the spread of those averages is the , and its standard deviation is the . For a mean it is the sample standard deviation divided by the square root of n, so quadrupling the sample only halves the error.
The central limit theorem says the sampling distribution of a mean is close to normal for large enough samples, even when the data is not, which is why many tests work.
Common trapconfusing the standard deviation, which describes how spread out the data is, with the standard error, which describes how precise your estimate is.
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Resources for this stage
Start with· follow one of these
- VideoFreeStatQuest with Josh Starmer
StatQuest · Beginner
Free: short, clear videos on each concept, from the normal distribution to p-values and power
- CourseFreeKhan Academy Statistics and Probability
Khan Academy · Beginner
Free: the probability, sampling distributions, confidence intervals and significance tests units, with practice
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