This applet simulates the taking of a random sample of three people from a large* population and recording their height (cm) or annual income ($).
Click ‘Do experiment’ to run the experiment once. You will see a sample taken one-by-one from the population and recorded on the dotplot and in the table. Click ‘Next step’ to proceed from one sample element to the next. Finally, the mean is calculated and recorded.
You can run the experiment up to four times, and each time the data will be recorded on the dotplot and in the table.
After you have run the experiment four times, you can click ‘Do 1000 experiments’ to repeat the experiment 1000 times. Watch the dotplots grow as the experiment is repeated. Click ‘Show theoretical distribution’ to add in the expected distribution for each of the random variables. How does the dotplot compare to the theoretical distribution?
* by assuming the sample is taken from a large population it is reasonable to assume that we are sampling with replacement.