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I have data for which I can compute a sample mean. These samples are certainly not random. Is there any way to make an estimate of the population mean from a single biased sample?

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  • $\begingroup$ How the sample was taken? If you want to estimate average age for the whole country and your sample consists only of primary school kids, then obviously you cannot use it. $\endgroup$ – Tim Jan 25 at 5:55
  • $\begingroup$ Just assume it's a biased sample. Is there absolutely no way to generalize from a biased sample? $\endgroup$ – Namenlos Jan 25 at 5:58
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    $\begingroup$ biased in what way? If everyone in your sample is 10 years old and you want to estimate age of general population, then you would probably be better with ignoring the sample when making your guess. $\endgroup$ – Tim Jan 25 at 6:41
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The only way I can think of is to use other characteristics of the data. Say, you have collected fields X, Y and Z, and field Z happens to be the height of people. You know the distribution of the height in the population from, say Wikipedia, and then re-weight each individuals so that their weighted distribution matches of the sample is identical to the height distribution of the population. If you don't have such data, I am afraid what you want to do is impossible

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  • $\begingroup$ That's what I feared. Thank you for your thoughts! $\endgroup$ – Namenlos Jan 25 at 18:48

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