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Knowing the average of a population, how could I evaluate an expected sample average based on k_sample?

Data Info:

Variance and standard deviation:

$\sigma^2= 0.18500975256337462$

$\sigma=0.43012760032736175$

population : 3572
value range : [0,60]
mean: 1.2140032642853837

Histogram : frequency (y) vs score value (x)
A few outsiders (x,y): (5,1),(8,1),(13,1) Histogram y:frequency & x:score value

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  • $\begingroup$ For absolute equality, unless all companies have the same value, $5000$. $\endgroup$ – André Nicolas Dec 4 '13 at 8:21
  • $\begingroup$ @AndréNicolas I understand but what about within x% of certainty? $\endgroup$ – Lazik Dec 4 '13 at 8:23
  • $\begingroup$ There are two numbers we need, the error allowed in how closely we approximate the true mean, and what probability of error is allowed (often this is $5\%$). And even given these numbers, we need some information about the variance. $\endgroup$ – André Nicolas Dec 4 '13 at 8:27
  • $\begingroup$ I can calculate the variance. Say the error allowed in how closely we approximate is alpha and the probability of error is sigma. What would be the math? $\endgroup$ – Lazik Dec 4 '13 at 8:31
  • $\begingroup$ Now we are at a more conventional problem. We need to assume the distribution is reasonable, so that we can use the Central Limit Theorem. If some detail is supplied, I should be able to give an answer tomorrow. $\endgroup$ – André Nicolas Dec 4 '13 at 8:40

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