Final answer:
When the variance of a payoff increases, it means that the possible outcomes are more spread out and less predictable. High school students typically encounter the concept of variance in statistics or probability courses.
Step-by-step explanation:
When the variance of a payoff increases, it means that the possible outcomes are more spread out and less predictable. In the context of probability and statistics, the variance measures the average squared deviation from the mean. Therefore, a higher variance indicates greater uncertainty and a wider range of potential outcomes.
For example, let's consider two investments. Investment A has a low variance, meaning that its payoffs are consistent and close to the expected value. On the other hand, Investment B has a high variance, indicating that its payoffs are more erratic and can deviate significantly from the expected value.
High school students typically encounter the concept of variance in statistics or probability courses, where they learn to measure and interpret variability in data sets. They will also explore how variance relates to other statistical measures, such as the standard deviation and the mean.