Short Answer

Weighted mean is a type of average where different values are given different levels of importance, called weights. Instead of treating all values equally, some values influence the result more than others.

For example, in exams, some subjects may have more marks than others. Weighted mean helps calculate the overall average by giving more importance to higher-mark subjects. It gives a more accurate result when all values are not equally important.

Detailed Explanation:

Weighted mean

Weighted mean is a special type of average used when all values in a dataset do not have the same importance. In normal mean (arithmetic mean), every value is treated equally. But in weighted mean, each value is multiplied by a weight, which shows its importance. This makes the result more accurate in real-life situations.

The idea behind weighted mean is simple. Some values contribute more to the final result than others. So, instead of just adding values, we multiply each value by its weight, then add all the results, and finally divide by the total of weights.

Meaning of weights

Weights are numbers that show how important each value is. A higher weight means more importance, and a lower weight means less importance.

For example, if a subject has more marks in an exam, it will have a higher weight. This means it will affect the final average more than a subject with fewer marks.

Formula of weighted mean

The formula of weighted mean is:
Weighted Mean = (Sum of value × weight) ÷ (Sum of weights)

This formula ensures that each value is counted according to its importance.

For example, suppose a student scores 80 marks in a subject with weight 2 and 70 marks in another subject with weight 1.
Step 1: Multiply values by weights → (80×2) + (70×1) = 160 + 70 = 230
Step 2: Add weights → 2 + 1 = 3
Step 3: Divide → 230 ÷ 3 = 76.67

So, the weighted mean is 76.67.

Importance of weighted mean

Weighted mean is important because it gives a more realistic average when values are not equally important. It reflects the true contribution of each value.

In many real-life situations, not all data points are equal. For example, in exams, some subjects carry more marks. In business, some products contribute more to sales. Weighted mean helps in such cases.

It is widely used in finance, education, and research because it provides a better and more accurate result.

Difference from simple mean

The main difference between weighted mean and simple mean is that simple mean treats all values equally, while weighted mean considers importance.

In simple mean, all values have equal effect on the result. In weighted mean, values with higher weights have more effect. This makes weighted mean more useful in practical situations.

Use in real life

Weighted mean is used in many real-life situations. In education, it is used to calculate final marks when different subjects have different weights.

In business, it is used to calculate average cost or profit where some items are more important. In finance, it is used to calculate average returns on investments.

It is also used in surveys and research where some responses are more important than others.

Advantages of weighted mean

Weighted mean has many advantages. It gives a more accurate average when values have different importance. It is useful in real-life situations and helps in better decision-making.

However, it requires proper knowledge of weights. If weights are not correct, the result may also be incorrect.

Conclusion

Weighted mean is an advanced form of average that considers the importance of each value. It gives more accurate results when values are not equally important. Because of its practical use, it is widely used in education, business, and research.