Imagine you're talking to someone who doesn't understand anything about statistics.You want to explain to them about the idea of sampling variation and inferencethe general idea of asampling distributionand what it means about the relationship between statistics and parameters. Write down what you'd tell them. Your answer should be a few paragraphsmy answer would probably be a page or soand it should include all of the following ideas. It shouldn't necessarily include these words, but should make some reference to the ideas and explain in non-technical terms what they mean.

• Statistics and parametersdifferences between them and relationship between them.
• The distribution of a statistic based on a population parameter.
• Some sense of how we quantify the amount of sampling variatione.g. the standard deviation of the distribution of sample statistics.
• The relationship between sample size and the amount of sampling variation.
• Inference: i.e. using a sample statistic to make some kind of conclusions about the population parameter, and what kinds of conclusions we can draw.

If you want to, you can use this example to illustrate your discussion:

In the American Community Survey, the Census Bureau surveys 60,000 households in the US. One of the questions they ask is how many people live in the house. In 2018 the answers had an average of 2.63 with a standard deviation of about 1. (This estimate of 1 isn't published, it's my own estimatetake it with a grain of salt but it's about right.)