Which statement correctly distinguishes a statistic from a parameter?

Which statement correctly distinguishes a statistic from a parameter?

• A. A statistic is derived from a sample; a parameter is derived from the population.
• B. A statistic is the population mean; a parameter is a sample mean.
• C. A statistic is always larger than a parameter.
• D. A statistic is a measure of dispersion; a parameter is a measure of central tendency.

Answer: (A)

The main idea is to distinguish where the numbers come from. A parameter describes a characteristic of the entire population, and a statistic describes the same kind of characteristic but for a sample drawn from that population. A parameter is fixed for a given population (though often unknown), while a statistic is computed from data in a sample and can vary if you take a different sample. That’s why the statement that a statistic is derived from a sample and a parameter from the population is the best description. For example, the true population mean is a parameter. If you take a sample and calculate its mean, that sample mean is a statistic. The two don’t have to be equal, and there’s no rule about one being larger or smaller than the other. Also, statistics and parameters can measure central tendency or dispersion; there isn’t a hard rule tying statistics to one kind of measure and parameters to another.

The main idea is to distinguish where the numbers come from. A parameter describes a characteristic of the entire population, and a statistic describes the same kind of characteristic but for a sample drawn from that population. A parameter is fixed for a given population (though often unknown), while a statistic is computed from data in a sample and can vary if you take a different sample. That’s why the statement that a statistic is derived from a sample and a parameter from the population is the best description.

For example, the true population mean is a parameter. If you take a sample and calculate its mean, that sample mean is a statistic. The two don’t have to be equal, and there’s no rule about one being larger or smaller than the other. Also, statistics and parameters can measure central tendency or dispersion; there isn’t a hard rule tying statistics to one kind of measure and parameters to another.