Short Answer
Weighted average is calculated by multiplying each value with its weight, adding all the results, and then dividing by the total of all weights. This method gives more importance to values with higher weights.
It is useful when different values do not have equal importance. The formula helps to get a more accurate average in situations like marks calculation, business data, and performance analysis.
Detailed Explanation:
Calculation of weighted average
The calculation of weighted average is used when different values have different levels of importance. In this method, each value is multiplied by a weight that shows its importance. After that, all the products are added together, and then the total is divided by the sum of all weights. This gives the weighted average.
Basic formula
The formula used for calculating weighted average is:
Weighted Average = (Sum of value × weight) ÷ (Sum of weights)
This formula ensures that values with higher weights affect the final result more.
Step by step process
To calculate the weighted average, we follow some simple steps. First, we write all the values along with their weights. Second, we multiply each value by its weight. Third, we add all the multiplied results to get the total. Fourth, we add all the weights. Finally, we divide the total of products by the total of weights to get the weighted average.
Example of calculation
Suppose we have two values: 70 and 90. The weights are 1 and 3 respectively. First, multiply values with weights: 70×1 = 70 and 90×3 = 270. Then add them: 70 + 270 = 340. Now add the weights: 1 + 3 = 4. Finally, divide 340 by 4. The weighted average is 85. This shows that the higher weighted value has more influence.
Importance of weights
Weights play a very important role in this calculation. They decide how much each value will affect the final average. A value with a higher weight contributes more, while a value with a lower weight contributes less.
Difference from simple calculation
In a simple average, all values are treated equally. But in weighted average, values are treated differently based on their importance. This makes the weighted average more useful in real-life situations.
Use in real life
Weighted average is used in many real-life situations. In education, different exams may have different weights. In business, products may have different quantities or importance. In such cases, weighted average gives a better result.
Accuracy in calculation
While calculating weighted average, it is important to multiply correctly and add all values and weights carefully. Any mistake in calculation can give a wrong result. So, each step must be done properly.
Conclusion
Weighted average is calculated by considering both values and their importance. It gives a more accurate result compared to simple average and is very useful in real-life situations where values are not equally important.