You should use a weighted mean instead of a regular arithmetic mean when some values are more important or represent larger groups (Gravetter et al., 2021). The arithmetic mean treats all values equally, but the weighted mean adjusts for differences in importance or sample size. For example, if a researcher wants to find the average test score for students from three schools with different numbers of students, a weighted mean would give a more accurate result. If School A has 200 students with an average score of 85, School B has 500 students with an average score of 78, and School C has 300 students with an average score of 82, a simple average would give 81.67. However, this ignores that School B has more students. A weighted mean would calculate the total scores based on the number of students, giving an average of 80.6, which better reflects the overall performance (Gravetter et al., 2021)