What is a weighted average in math?
A weighted average is an average in which some values count more than others. Multiply each value by its weight, add those products, and divide by the sum of the weights. Course grades, GPAs and combined groups use it, because a plain mean would treat every value as equally important.
Weighted Average in a picture
Formal definition and notation
For values x1, …, xn with nonnegative weights w1, …, wn (not all zero), the weighted average is x̄w = w1x1 + w2x2 + ⋯ + wnxnw1 + w2 + ⋯ + wn. When the weights are percents or fractions that add to 1, the denominator is 1 and the weighted average is just the sum of the products. With equal weights it is the ordinary mean.
| Symbol | Read it as | Meaning |
|---|---|---|
| wi | w sub i | the weight of the ith value: a percent, a number of credits, a count or a quantity |
| x̄w | x bar sub w | the weighted mean |
| Σ wixi | the sum of w i times x i | add every weight-times-value product |
Key facts
- A weight of 3 counts a value as if it appeared 3 times in the list.
- The weighted average is pulled toward the values with the biggest weights.
- It always lies between the smallest and largest values.
- Divide by the sum of the weights, not by the number of values.
- With equal weights, the weighted average equals the ordinary mean.
- Mixture and combined-group problems are weighted averages: the weights are the amounts or group sizes.
Weighted average formula
- xi
- each value (a score, a grade point, a price)
- wi
- how much that value counts
- Σ
- add over all the values
If the weights are percents that add to 100%, write them as decimals that add to 1 and skip the division.
Try it: weights as repeats
A score of 90 with weight 3 is the same as listing 90 three times. Here 80 has weight 1 and 90 has weight 3, so the mean is 87.5. Add or remove a 90 to change its weight.
Weighted Average examples, step by step
Example 1: A course grade
Homework counts 20% of a grade, tests 50% and the final exam 30%. Lena has 95 on homework, 80 on tests and 70 on the final. What is her course grade?
- Write the weights as decimals: 0.20, 0.50 and 0.30. They add to 1.
- Multiply: 0.20 × 95 = 19, 0.50 × 80 = 40, 0.30 × 70 = 21.
- Add: 19 + 40 + 21 = 80.
Answer: Her course grade is 80.
Example 2: A grade point average
Omar earns an A (4.0) in a 4-credit class, a B (3.0) in a 3-credit class and a C (2.0) in a 1-credit class. What is his GPA?
- Weight each grade point by its credits: 4 × 4.0 = 16, 3 × 3.0 = 9, 1 × 2.0 = 2.
- Add the products: 16 + 9 + 2 = 27.
- Add the weights: 4 + 3 + 1 = 8 credits.
- Divide: 278 = 3.375.
Answer: His GPA is 3.375.
Example 3: A coffee blend
A shop mixes 2 pounds of coffee that costs 9 dollars per pound with 6 pounds that costs 5 dollars per pound. What is the price per pound of the blend?
- The weights are the amounts: 2 pounds and 6 pounds.
- Total cost: 2 × 9 + 6 × 5 = 18 + 30 = 48 dollars.
- Total weight: 2 + 6 = 8 pounds.
- Price per pound: 488 = 6.
Answer: The blend costs 6 dollars per pound, closer to 5 because there is more of the cheaper coffee.
Common mistakes
Tests count for half the grade, so the 80 must pull harder than the homework score.
The denominator is the sum of the weights. A GPA of 9 on a 4-point scale is impossible, which shows the error.
There is three times as much of the 5-dollar coffee, so the blend price lands nearer to 5.
Not to be confused with
The simple mean gives every value weight 1. For 80 and 90 it is 85; with weights 1 and 3 the weighted average is 87.5.
The median is the middle of the ordered values and ignores how big the other values are. The weighted average uses every value and its weight.
Quick check: 3 questions
A quiz score of 70 has weight 1 and a test score of 100 has weight 2. What is the weighted average?
Answer: B. 1 × 70 + 2 × 1001 + 2 = 2703 = 90. 85 is the plain mean, 270 forgets to divide, and 135 divides by 2 values instead of 3 total weight.Show answer and explanation
Labs count 40% and exams 60%. A student scores 85 on labs and 75 on exams. What is the final grade?
Answer: C. 0.4 × 85 + 0.6 × 75 = 34 + 45 = 79. 80 is the plain mean, 81 swaps the weights, and 160 adds the scores.Show answer and explanation
Values 10 and 20 have weights 1 and 4. Where is the weighted average?
Answer: C. 1 × 10 + 4 × 205 = 905 = 18, closer to 20 because 20 has more weight. It cannot go above the largest value, 20.Show answer and explanation
Weighted Average: frequently asked questions
How do you calculate a weighted average with percentages?
Change each percent weight to a decimal, multiply it by its score, and add the products. If the percents add to 100%, you are done; there is nothing to divide. Example: 30% at 90 and 70% at 80 gives 0.3 × 90 + 0.7 × 80 = 27 + 56 = 83.
When should you use a weighted average instead of a regular average?
Use it whenever the values do not all count equally: grade categories with different percents, classes with different credits, groups of different sizes, or mixtures with different amounts. If every value counts the same, the weights are equal and the regular average gives the same answer.
Practice and tools
Sources
- Wolfram MathWorld, Weighted Mean
- OpenStax, Introductory Statistics 2e, 2.5 Measures of the Center of the Data
Updated November 2026·Reviewed by the Effortless Math team·Standards: n/a
Cite this entry
Effortless Math Team. “Weighted Average.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/weighted-average/
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