Weighted Average
Calculator for weighted average – for finance, statistics, and data analysis.
Applications - finance (portfolio average price), statistics (weighted data average), academic grading (GPA with course credits).
Decimal numbers - the calculator supports decimal numbers. Use a comma or period as the decimal separator.
Bulk import - paste a list of values separated by spaces into the first field. Do the same for weights.
Ergebnis
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Applications - finance (portfolio average price), statistics (weighted data average), academic grading (GPA with course credits).
Decimal numbers - the calculator supports decimal numbers. Use a comma or period as the decimal separator.
Bulk import - paste a list of values separated by spaces into the first field. Do the same for weights.
Formula for the weighted average
The mathematical formula for calculating the weighted average.
Weighted Average = (Value1 × Weight1 + Value2 × Weight2 + ...) / (Weight1 + Weight2 + ...).
Example: (8 × 2 + 6 × 1 + 9 × 3) / (2 + 1 + 3) = 49 / 6 = 8.17
All values are multiplied by their respective weights, the products are summed, and divided by the sum of all weights.
What is the weighted average?
The weighted average is a calculation where different values have different significance (weights).
Unlike the simple arithmetic mean, where all values are treated equally, the weighted average considers that some values are more important than others.
This is especially useful for school grades (where exams count more than homework), financial calculations (where larger investments have more weight), or in statistics.
Practical application examples
How the weighted average is used in different areas.
- School grades: Exams often count double or triple compared to oral grades or homework.
- University grades: Modules are weighted by ECTS credits. A module with 10 ECTS has more influence on the average than one with 5 ECTS.
- Finance & Investment: When calculating the average return of a portfolio, individual investments are weighted by their share.
Frequently asked questions about weighted average
- What is the difference between arithmetic and weighted average?
- The arithmetic average adds all values and divides by the count. The weighted average also considers the importance (weight) of each value - values with higher weight influence the result more.
- How do I calculate the weighted average in Excel?
- In Excel, use the formula =SUMPRODUCT(Values,Weights)/SUM(Weights). Example: =SUMPRODUCT(A1:A3,B1:B3)/SUM(B1:B3) calculates the weighted average of values in A1:A3 with weights in B1:B3.
- Does the sum of weights need to equal 100%?
- No, weights can be any positive numbers (1, 2, 3 or 10%, 30%, 60%). The formula divides by the sum of weights, so the result is correct regardless of the scale used.
- When should I use weighted instead of arithmetic average?
- Use the weighted average when individual values have different importance or represent different sized groups, e.g., for grades with different subject weightings.
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