Timeline for Question about standard deviation and central limit theorem
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2020 at 10:19 | answer | added | Sextus Empiricus | timeline score: 1 | |
| Jul 1, 2014 at 1:28 | comment | added | Glen_b | Under appropriate conditions, you can apply the CLT to the variance (e.g. see p3-4 here). | |
| Jun 30, 2014 at 19:00 | history | edited | Alecos Papadopoulos | CC BY-SA 3.0 |
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| Jun 27, 2014 at 0:39 | comment | added | Glen_b | "The CLT says that if I measure the mean of a set of values a sufficiently large number of times these means will follow a normal distribution." --- well, actually, that's not quite what any of the versions of the CLT say. The quote from Wikipedia* is closer to accurate (but the claim is strictly speaking false - the CLT doesn't quite say that either). $\quad\quad\quad\quad$ *(not 'wiki' - that's a bit like calling the Library of Congress 'building' when referring to it) | |
| Jun 26, 2014 at 19:23 | answer | added | paul | timeline score: 11 | |
| Jun 26, 2014 at 18:29 | comment | added | whuber♦ | @Gene That can be used to demonstrate a special case: because the sampling distribution of the SD from a Normal population is $\chi^2$, which asymptotically is Normal, a CLT-like result holds in this case. However, when sampling from a Bernoulli$(1/2)$ variate, the sampling distribution of the SD does not approach normality. | |
| Jun 26, 2014 at 18:22 | comment | added | Gene Arboit | Would mathworld.wolfram.com/StandardDeviationDistribution.html be relevant? | |
| Jun 26, 2014 at 17:42 | history | edited | user49060 | CC BY-SA 3.0 |
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| Jun 26, 2014 at 17:36 | history | edited | whuber♦ | CC BY-SA 3.0 |
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| Jun 26, 2014 at 16:27 | comment | added | user49060 | I am sorry, perhaps what I wrote was confusing. The CLT says that if I measure the mean of a set of values a sufficiently large number of times these means will follow a normal distribution. My question is instead if I took the same data set but calculated the sample standard deviation would these values come from a normal distribution? I.e., can the CLT be applied to moments beyond the first moment? Please let me know if this clears up any confusion. Thanks for your help. | |
| Jun 26, 2014 at 15:43 | review | First posts | |||
| Jun 26, 2014 at 15:50 | |||||
| Jun 26, 2014 at 15:25 | history | asked | user49060 | CC BY-SA 3.0 |