Demonstrating the Central Limit Theorem. 1000 pieces of scores, roughly normally distributed $N(50, 15.8)$. Students draw 10 random pieces with replacement to find the mean.
Notice how the sampling distribution of the means builds up. According to theory, the mean of these sample means should be close to the population mean ($\mu \approx 50$), and the standard deviation of these sample means (the true Standard Error) is calculated using the population standard deviation: $\sigma / \sqrt{n} = 15.8 / \sqrt{10} \approx 5.00$.
However, in reality, we rarely know the population standard deviation ($\sigma$). Instead, we estimate the Standard Error using the sample standard deviation ($s$). This simulation calculates the estimated standard error for each individual sample ($s / \sqrt{n}$) to show how its average approaches the theoretical standard error and matches the empirical standard deviation of the means.