What term describes the pattern of sample means that would occur if many samples are drawn from the population?

What term describes the pattern of sample means that would occur if many samples are drawn from the population?

• A. Sampling distribution of the mean
• B. Population distribution
• C. Theoretical distribution of the median
• D. Sampling distribution of the variance

Answer: (A)

The pattern you’d see if you drew many samples from a population and computed each sample’s mean is the sampling distribution of the mean. This distribution shows how sample means vary due to random sampling and is centered at the true population mean. Its spread is the standard error, typically sigma divided by the square root of the sample size, so larger samples produce more precise estimates. By the central limit theorem, this distribution is approximately normal for large samples, even if the population itself isn’t normally distributed. The other ideas refer to different quantities: the population distribution concerns individual values in the population, the median’s distribution concerns medians rather than means, and the sampling distribution of the variance focuses on variances across samples.

The pattern you’d see if you drew many samples from a population and computed each sample’s mean is the sampling distribution of the mean. This distribution shows how sample means vary due to random sampling and is centered at the true population mean. Its spread is the standard error, typically sigma divided by the square root of the sample size, so larger samples produce more precise estimates. By the central limit theorem, this distribution is approximately normal for large samples, even if the population itself isn’t normally distributed. The other ideas refer to different quantities: the population distribution concerns individual values in the population, the median’s distribution concerns medians rather than means, and the sampling distribution of the variance focuses on variances across samples.