Which statement correctly distinguishes a population parameter from a sample statistic?

• A. A statistic describes the population; a parameter estimates a sample.
• B. A parameter describes the population; a statistic estimates a parameter from a sample.
• C. Both refer to the same concept.
• D. Parameter describes the population; a statistic estimates a parameter from a sample.

Answer: (D)

In statistics, a population parameter is a fixed value that describes a characteristic of the entire population, like the true mean μ or true proportion p. That value is usually unknown because we can’t measure everyone in the group. A sample statistic, on the other hand, is a number calculated from a sample, such as the sample mean x̄ or sample proportion p̂, and its purpose is to estimate the population parameter.

So the correct idea is that a parameter describes the population, while a statistic estimates that parameter from a sample. For instance, the population mean describes the population, and the sample mean from a subset of data is used to estimate that mean. This distinction explains why statistics vary from sample to sample, whereas the population parameter remains fixed (though typically unknown).