Weighted Average Calculator
What a Weighted Average Is
A weighted average gives each number its own importance instead of treating them all equally. Teachers grading tests, analysts combining survey results, and investors tracking returns rely on it when some inputs matter more.
Formula and Worked Example
Multiply every value by its weight, add those products, then divide by the total weight. For grades of 80 and 90 weighted 2 and 3, that is (80 x 2 + 90 x 3) / 5 = 430 / 5 = 86.
The plain average would be 85, so the heavier weight on 90 nudges the result up to 86. Equal weights of 1 on each value collapse the formula back to a normal average.
A portfolio shows why the weighting matters in practice. An investor holding 6,000 in a fund returning 4 percent and 2,000 in a fund returning 11 percent enters the pairs with the dollar amounts as weights, giving (6,000 x 4 + 2,000 x 11) / 8,000 = 46,000 / 8,000 = 5.75 percent. Treating the two returns equally instead would report 7.5 percent, overstating real performance by nearly two points. Course grades behave the same way: a 5-credit lab scored 92 and a 2-credit seminar scored 78 give (460 + 156) / 7 = 88, not the 85 a flat average reports.
Entering Your Pairs
Add each pair to the Values (x,w) input, listing the value first and its weight second, then press Calculate. Keep units consistent: mixing a 0-1 weight scale with 1-5 ratings skews the result. Weights need not sum to 100 because the calculator divides by whatever total it sees.
Frequently Asked Questions
How is the weighted average 86 found?
Multiply each score by its weight and add the products: 80 x 2 plus 90 x 3 gives 430. Dividing by the weight total of 5 produces 86.
What weights give a simple average?
Choose identical weights, such as 1 and 1 or 50 and 50. With 80 and 90 both weighted 1, the sum of 170 divided by 2 equals 85, the ordinary mean.
Can the weights be percentages?
Yes, as long as they are positive. Entering 70 weighted 0.4 and 90 weighted 0.6 computes (28 + 54) / 1 = 82, and the division by the weight sum keeps the scale consistent.
Where is a weighted average useful?
Anywhere some values should dominate, like GPA where a 4-credit A pulls harder than a 1-credit seminar, or portfolio returns where one large holding matters more than a small one.
Does the order of entries matter?
No, because addition and multiplication commute. Pairs of 80 with weight 2 and 90 with weight 3 total 430 whether you list them in either order, and dividing by 5 still returns 86.