Questions: Compared to small samples, large samples have variability.

Solution Steps

To determine the variability of large samples compared to small samples, we can use the concept of the law of large numbers. As the sample size increases, the sample mean tends to get closer to the population mean, which implies that the variability decreases.

In statistics, variability refers to how spread out the values in a data set are. For samples, larger sample sizes tend to provide a more accurate estimate of the population parameters, leading to reduced variability in the sample statistics.

According to the law of large numbers, as the sample size \( n \) increases, the sample mean \( \bar{x} \) approaches the population mean \( \mu \). This means that the variability of the sample mean decreases as \( n \) increases, leading to a more stable estimate.

Given that larger samples yield a more accurate representation of the population, we conclude that large samples have less variability compared to small samples.

Final Answer