Final answer:
The average information learned from a set with a uniform distribution is at its maximum since all outcomes are equally likely. A uniform distribution is defined by the equality of probability for all outcomes. However, surveying people on a campus for the average educational level may result in a distorted outcome due to a selection effect, as this does not represent a uniform or random sample of the entire nation's population.
Step-by-step explanation:
If a set has a uniform distribution, the average information learned after knowing the outcome of the selection can be measured in terms of Shannon entropy. In the context of a uniform distribution, every outcome is equally likely, which means that the amount of surprise or information gained from any particular outcome is the same across all outcomes. Therefore, the average information or entropy is maximum, as there is no way to predict which outcome is more likely than another. This is because a uniform distribution indicates no bias towards any outcome, and each outcome contributes equally to the average information.
However, when you conflate the uniform distribution of probabilities with the actual process of surveying a population for the average educational level, the two are not directly related. While the uniform distribution talks about probabilities, the surveying of a population for its average educational level involves a sampling process which should aim to be as random and representative as possible to avoid a selection effect. If only people on a campus are surveyed, then the results may be distorted by a selection effect since the campus population may not be representative of the nation's overall educational level.