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CalcGospel 國際數學圖譜

Central Limit Theorem Visualizer

Sampling distributions and convergence of the sample mean

中文辅助说明

选择均匀、二项、泊松、指数或双峰总体,再改变样本容量和模拟次数,就能观察样本均值的直方图如何逐渐形成。它特别适合比较“原总体的形状”和“样本均值分布的形状”,直观看出样本容量增大时,样本均值为什么会越来越接近正态分布。

Simulation Settings

30
1000
105000

Population Distribution (X)

Sampling Distribution of Sample Mean

Central Limit Theorem (CLT) The Central Limit Theorem (CLT) states that, regardless of the population distribution, the sampling distribution of the sample mean will tend toward a Normal distribution as the sample size becomes sufficiently large (typically n ≥ 30):