Could you please give me an example of gathering a set of data and choosing a small sample, between 10 and 20 pieces of data, and a simple value to measure, such as the ages of visitors in a park?

You just gave an example. Go ask 20 visitors their age. That's probably not a good example, since it's fairly hard to pick truly random people. But, you might count the number of people entering or leaving in a certain time period, and tracking that value over the course of a day.