How to calculate a weighted average?
To calculate a weighted average, multiply each value by its weight (coefficient), sum all these products, then divide the total by the sum of all the weights. This is crucial when some data points are more important than others.
Explanation
A weighted average is used when the elements in a series do not all have the same importance. For example, for school grades, a final exam might have a higher weight than a homework assignment.
Steps to calculate a weighted average:
- Associate each value with its weight: Each data point must have an assigned weight.
- Multiply each value by its weight: Perform this operation for each (value, weight) pair.
- Sum all the results of these multiplications: This is the sum of the weighted products.
- Sum all the weights: Calculate the total sum of the weights.
- Divide the sum of the weighted products by the sum of the weights: The result is your weighted average.
Formula / method
Weighted Average = (v1w1 + v2w2 + ... + vn*wn) / (w1 + w2 + ... + wn)
Where:
vrepresents each valuewrepresents the weight associated with each value
Concrete example
Example: Calculating a student's average grade
A student obtained the following grades with their respective weights:
- Mathematics: 12/20 (weight 3)
- French: 15/20 (weight 2)
- History: 10/20 (weight 1)
- Multiply each grade by its weight:
- Mathematics: 12 * 3 = 36
- French: 15 * 2 = 30
- History: 10 * 1 = 10
- Sum the weighted products:
- 36 + 30 + 10 = 76
- Sum the weights:
- 3 + 2 + 1 = 6
- Divide the sum of products by the sum of weights:
- 76 / 6 = 12.67
The student's weighted average is 12.67/20.
Common mistake
Do not confuse the weighted average with the simple average. The simple average assumes all elements have the same weight (a weight of 1 for all). Using the wrong method can significantly distort your result.
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