Timeline for central limit theorem: do we care about standard deviation within one sample of size n? [duplicate]
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Apr 26, 2019 at 15:39 | vote | accept | Kid_Learning_C | ||
| Apr 26, 2019 at 10:17 | history | closed |
Xi'an Glen_b |
Duplicate of Do we use the SD of whole population or SD of just one sample to calculate SE of samples means in central limit theorem? | |
| Apr 26, 2019 at 7:20 | comment | added | corey979 | (...) i.e. the error, uncertainty about its exact value is smaller and smaller. In a quite flat distribution, like $N(0,100)$, it's relatively less ambiguous where the mean is when compared to $N(0,1)$. So SD is a feature of a distribution as a whole, and SE is the measure of uncertainty of a single parameter of it. | |
| Apr 26, 2019 at 7:18 | comment | added | corey979 | SD, in general, is a characteristic of a distribution, roughly speaking: how wide it is. SE of the mean says how precise the estimation of the mean is. Consider two exact Gaussians, $N(0,1)$ and $N(0,100)$. The means are known exactly in both cases, one cannot write it's $0\pm 1$ neither $0\pm 100$. Now consider a sample, say of two points. They can well be drawn from the tail of the distribution, so those could be $(40,60)$. The mean is 50, how close is it to the true value, zero? Consider also $(-10,100)$, or $(-10,10)$ etc. The more data you draw, the better the mean is constrained, (...) | |
| Apr 26, 2019 at 6:55 | review | Close votes | |||
| Apr 26, 2019 at 10:20 | |||||
| Apr 26, 2019 at 6:47 | answer | added | Isam Abdullah | timeline score: 1 | |
| Apr 26, 2019 at 6:43 | comment | added | Kid_Learning_C | @corey979 Thanks, but I'm confused: what's the difference between SE of the mean vs SD of those 8888 means? I've re-editted my question with more clear names. Could you point out which is value #1 and which is value #2 ? | |
| Apr 26, 2019 at 6:41 | history | edited | Kid_Learning_C | CC BY-SA 4.0 |
added 18 characters in body
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| Apr 26, 2019 at 6:34 | comment | added | corey979 | The standard deviation of the population is the true value, you either know it or not. Estimators are used to estimate it. The underlying distribution might be, or might not be Gaussian, e.g. for skewed distributions the mean, mode and median are different, so the sd might be quite shifted. The formula for SE is the SE of the mean; the SD is the SD of the distribution of your n=8888 means. | |
| Apr 26, 2019 at 6:33 | answer | added | Noah | timeline score: 1 | |
| Apr 26, 2019 at 6:25 | history | asked | Kid_Learning_C | CC BY-SA 4.0 |