The weighted mean is used when different data points have varying degrees of importance or influence on the overall average. It takes into account the weights assigned to each data point, reflecting their relative significance in the dataset. In a hypothetical study involving student grades, where different assignments or exams are worth different percentages of the final grade, using a weighted mean would be appropriate. For example, consider a course where quizzes are worth 20% of the final grade, midterm exams are worth 30%, and a final project is worth 50%. In this scenario, the grades on each component would be weighted accordingly when calculating the overall average for the course. This ensures that each assessment contributes proportionally to the final grade, reflecting its importance in assessing the students' performance. Using the arithmetic mean in this situation would not accurately represent the central tendency because it would treat all data points equally, regardless of their significance. Therefore, the weighted mean is the best representation of central tendency when different data points have varying degrees of importance or influence