The best answer is B. As a sample size grows, its mean gets closer to the average of the whole population.
The law of large numbers, in probability and statistics, states that as a sample size grows, its mean gets closer to the average of the whole population. This is due to the sample being more representative of the population as it increases in size. The law of large numbers guarantees stable long-term results for the averages of some random events1
A. As a sample size decreases, its standard deviation gets closer to the average of the whole population is not correct, because it confuses the concepts of standard deviation and mean. Standard deviation is a measure of how much the values in a data set vary from the mean, not how close the mean is to the population average. Also, as a sample size decreases, its standard deviation tends to increase, not decrease, because the sample becomes less representative of the population.
C. As a sample size decreases, its mean gets closer to the average of the whole population is not correct, because it contradicts the law of large numbers. As a sample size decreases, its mean tends to deviate from the average of the whole population, because the sample becomes less representative of the population.
D. When a sample size doubles, the sample is indicative of the whole population is not correct, because it does not specify how close the sample mean is to the population average. Doubling the sample size does not necessarily make the sample indicative of the whole population, unless the sample size is large enough to begin with. The law of large numbers does not state a specific number or proportion of samples that are indicative of the whole population, but rather describes how the sample mean approaches the population average as the sample size increases indefinitely.
