Weighted Average vs Simple Average

Weighted average and simple average are two methods of calculating the mean of a set of values. The main difference between them is that in a weighted average, each value is given a weight based on its importance or frequency, while in a simple average, all values are given equal weight.

Weighted Average

In a weighted average, each value is considered as many times as it occurs, but its contribution to the final mean is proportional to its weight. The weight can be based on any factor, such as frequency, importance, or relevance.

For example, if we have a set of test scores with the following values and frequencies:

- 80 (3 times)
- 90 (2 times)
- 70 (1 time)

To calculate the weighted average, we need to assign a weight to each value based on its frequency. In this case, the weights would be:

- 80 (weight = 3)
- 90 (weight = 2)
- 70 (weight = 1)

Then, we can calculate the weighted average using the formula:

weighted average = (value1 x weight1 + value2 x weight2 + ... + valueN x weightN) / (weight1 + weight2 + ... + weightN)

In this example, the weighted average would be:

weighted average = (80 x 3 + 90 x 2 + 70 x 1) / (3 + 2 + 1) = 81.67

Simple Average

In a simple average, all values are given equal weight, regardless of their frequency or importance. The formula for calculating the simple average is:

simple average = (value1 + value2 + ... + valueN) / N

Using the same example as before, the simple average would be:

simple average = (80 + 90 + 70) / 3 = 80

Conclusion

In summary, each value is considered as many times as it occurs in a weighted average, while in a simple average, all values are given equal weight. The choice between these two methods depends on the purpose of the analysis and the nature of the data.