Means can have an estimate {estimate} {estimation}|.
Intervals {confidence interval}| around estimated means have a confidence level that population mean is in the interval. Unbiased estimate can have 95% confidence if low estimate equals x - (1.96 * s) / N^0.5 and high estimate equals x + (1.96 * s) / N^0.5, where x is mean, s is standard deviation, and N is sample size.
On average, situations have sets of expected outcomes {expectation, statistics} {expected value}|. Averaging outcome values can find expected value: sum from i = 1 to i = N of (w(i) * p(i)) / N, where N is number of values, w(i) is outcome worth, and p(i) is outcome probability.
Average is not the best estimate {Stein's paradox} {Stein paradox}. Best estimate is average plus factor times difference between average and grand average: e = u * f * (u - U). Factor depends on standard deviation, as shown by Bayes.
Estimates have population, which sets correct confidence interval {unbiased interval}. Sample means are unbiased population-mean estimates. Sample variances are unbiased population-variance estimates.
3-Statistics-Statistical Population
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Date Modified: 2022.0225