Weighted Average — Definition

Definition

Weighted Average is a method of calculating the average where different values are given different levels of importance or 'weight'. Think of it like this: if you're calculating your overall exam score and the written exam is worth 70% while the practical is worth 30%, you can't just add the two scores and divide by 2.

Instead, you need to give more importance to the written exam score because it carries more weight. This is exactly what weighted average does - it considers the relative importance of each value while calculating the final average.

For UPSC CSAT aspirants, understanding weighted average is crucial because it appears in various question types including mixture problems, age-related questions, and marks calculation scenarios. The key difference from simple average is that in simple average, all values are treated equally (each has weight 1), while in weighted average, different values have different weights based on their importance or quantity.

For example, if a class has 20 students with an average score of 80 and another class has 30 students with an average score of 70, the combined average is not simply (80+70)/2 = 75. Instead, we need to consider the weight (number of students) of each class.

The weighted average would be (20×80 + 30×70)/(20+30) = (1600+2100)/50 = 74. This concept becomes particularly important in CSAT when dealing with problems involving mixtures of different quantities, calculating overall percentages, or determining combined rates.

The weighted average always lies between the highest and lowest values being averaged, and it's pulled toward the value with the highest weight. Understanding this concept thoroughly will help you solve complex problems involving ratios, proportions, and mixtures more efficiently in the CSAT exam.