A statistic is a generalization concerning an entire sample, such as the mean, mode, or median. A parameter is a generalization for an entire population, such as the mean, mode, or median. In order to get a parameter, the entire population is involved, whereas a statistic is derived from a sample of that population.
There is an infinite number of samples that can be taken from a large population. One sample from a population might yield a slightly different statistic than another sample taken from the same population, but the statistics should be similar to each other. If more and more samples of the same size were taken from the population, the sampling distribution of the statistic would resemble a bell curve or normal distribution.
The average of the sampling distribution is essentially equivalent to the parameter. The standard deviation of the sampling distribution, called sampling error, tells us something about how different samples would be distributed which, in turn, tells how far the statistic is from the parameter. A low sampling error means that we have relatively less variability or range in the sampling distribution and are therefore closer to the parameter.
"Q&A: Sample vs. population" is a series of questions and answers about statistics written for teachers and students. The questions are ones that students might ask while studying statistics. Teachers can use this Q&A to gain additional knowledge about statistics, or use it in the classroom as outlined below.
• An engagement activity. Use selected questions to start a discussion.
• An inquiry tool. Use selected questions and answers to help students generate questions. Propose a question, such as "How does a statistic differ from a parameter?" Have students read the answer to the question and write down 3–5 questions they would like answered as a result of reading the material.
• A source of information. Students can use the questions and answers as part of their research on statistics.
• A form of review. Use the questions as a review at the end of a unit on statistics.
• A follow-up. Have students read the questions and answers to gain additional information about statistics following a related activity.
Online Exploration: Galaxy Hunter