Draw repeated samples from a hidden population and watch the sample means cluster. Discover how standard error measures that spread, and explore the core properties that make a good estimator: bias, consistency, and efficiency.
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Population
Population of measurements N(μ, 20) (true mean hidden)
Sample Size (n)
Draw Samples
Sample means cluster around the true population mean
Larger samples produce tighter clustering of sample means: smaller SE
n = 20
n = 100 (theoretical)
n = 20
SE = 4.472
n = 100
SE = 2.000
55% smaller
Doubling n reduces SE by a factor of √2 ≈ 1.41. To halve the SE, you need 4× the sample size.
An estimator is unbiased if its expected value equals the true parameter. The sample mean x̄ is unbiased: E[x̄] = μ
Unbiased Estimator (x̄)
Biased Estimator (+10)
Unbiased
Dots center on μ = 100. The average of many estimates equals the true value.
Biased (+10)
Dots center on 110. Systematically misses the true value, even with many samples.