Definition: A population is the entire group you want to learn about, and a sample is the smaller part of it that you actually study.
What are they?
The population is everyone or everything of interest, like all sixth graders in a district. A sample is a part of it that you measure.
Why sample?
Counting everyone takes too long or costs too much. A pollster does not ask all 50 million voters. A sample of a few thousand, chosen well, can estimate the whole.
How do you make an inference?
Scale up the sample result. Mathbot samples 60 bulbs from a batch of 4,500, and finds 3 defective. That is 5 percent, so the estimate is 0.05 x 4,500 = 225 defective bulbs.
What makes a sample good?
It must be random and representative, and reasonably large. Several samples will give slightly different estimates, which shows the natural variation in sampling.
What is a common mistake?
Claiming the estimate is exact. The sample result is only a prediction. Another error is generalizing beyond the population you sampled: results from one school do not describe all schools.