Create a diverse set of five math problems that require students to apply concepts of probability and statistics, ensuring that at least one problem involves calculating probabilities, one problem requires analyzing a data set, and another utilizes statistical measures such as mean, median, and mode; also, provide constructive feedback emphasizing the importance of using multiple strategies for problem-solving.
Please help me to create a set of diverse math problems that require students to use algebraic expressions, ensuring to include various levels of complexity. Include problems that involve solving equations, simplifying expressions, and utilizing variables, while also providing feedback prompts that encourage students to explore different strategies for solving each problem.