I took \(100\) samples of \(3\) from a population with a parametric mean of \(5\) (shown by the blue line). 3.3.2 Means of 100 random samples (N=3) from a population with a parametric mean of 5 (horizontal line). About two-thirds (\(68.3\%\)) of the sample means would be within one standard error of the parametric mean, \(95.4\%\) would be within two standard errors, and almost all (\(99.7\%\)) would be within three standard errors. If you take many random samples from a population, the standard error of the mean is the standard deviation of the different sample means. One way to do this is with the standard error of the mean.
Once you've calculated the mean of a sample, you should let people know how close your sample mean is likely to be to the parametric mean. With \(20\) observations per sample, the sample means are generally closer to the parametric mean. The second sample has three observations that were less than \(5\), so the sample mean is too low. The first sample happened to be three observations that were all greater than \(5\), so the sample mean is too high. 3.3.1 Individual observations (X's) and means (red dots) for random samples from a population with a parametric mean of 5 (horizontal line).Īs you can see, with a sample size of only \(3\), some of the sample means aren't very close to the parametric mean. The \(X's\) represent the individual observations, the red circles are the sample means, and the blue line is the parametric mean. Here are \(10\) random samples from a simulated data set with a true (parametric) mean of \(5\). If your sample size is small, your estimate of the mean won't be as good as an estimate based on a larger sample size. Your sample mean won't be exactly equal to the parametric mean that you're trying to estimate, and you'd like to have an idea of how close your sample mean is likely to be.
When you take a sample of observations from a population and calculate the sample mean, you are estimating of the parametric mean, or mean of all of the individuals in the population.
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