Which statement correctly contrasts statistics and parameters in terms of their scope?

Which statement correctly contrasts statistics and parameters in terms of their scope?

• A. Statistics are numerical values based on the sample; parameters are numerical values based on the population
• B. Statistics are the entire group; parameters are a subset
• C. Statistics use Greek letters; Parameters use English letters
• D. Statistics are fixed; parameters vary with samples

Answer: (C)

The main idea here is the distinction between population and sample quantities. A parameter is a numerical value that describes a characteristic of the entire population (for example, the population mean or standard deviation). A statistic is the corresponding value computed from a sample drawn from that population (like the sample mean or sample standard deviation). Because a sample can be different each time, statistics can vary from one sample to another, while the population parameter is fixed for that population. So, the correct way to think about scope is: parameters describe the population; statistics describe the sample. Notation-wise, standard practice uses Greek letters for population parameters (mu, sigma, etc.) and Latin letters for sample statistics (x-bar, s, p-hat, etc.), so focusing on the letters in a statement can be misleading. The notion that statistics are based on the sample and parameters on the population captures the essential contrast in scope.

The main idea here is the distinction between population and sample quantities. A parameter is a numerical value that describes a characteristic of the entire population (for example, the population mean or standard deviation). A statistic is the corresponding value computed from a sample drawn from that population (like the sample mean or sample standard deviation). Because a sample can be different each time, statistics can vary from one sample to another, while the population parameter is fixed for that population.

So, the correct way to think about scope is: parameters describe the population; statistics describe the sample. Notation-wise, standard practice uses Greek letters for population parameters (mu, sigma, etc.) and Latin letters for sample statistics (x-bar, s, p-hat, etc.), so focusing on the letters in a statement can be misleading. The notion that statistics are based on the sample and parameters on the population captures the essential contrast in scope.