Weighted Average
Provide pairs: a value and its weight, one pair per line. The result reflects the different importance of each item.
How to use this page
- Fill in the fields in the form above — the result recomputes at once, with no page reload.
- Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
- The formula we use is shown lower on this page — you can check the arithmetic yourself.
- To compute the same for another game or variant, change it in the select field — prices and pools update automatically.
What this page does not do: It does not point to numbers to play and does not predict a draw — every draw is independent of the previous ones.
Further reading
A weighted average differs from a plain average in that each value has an assigned weight. You sum the products of value times weight, then divide by the sum of the weights alone. With equal weights, the weighted average and the arithmetic mean give the same number — the arithmetic mean is simply a special case of the weighted one.
An example with grades. Suppose there are three grades: 5 with weight 3, 4 with weight 2, and 3 with weight 1. You multiply: 5 times 3 is 15, 4 times 2 is 8, 3 times 1 is 3. Together, 26 divided by 6 gives 4.33. A plain arithmetic average of these grades would give 4.0, which is a third of a grade lower. The five weighed the most and pulled the result upward.
This same method works outside of school. You calculate the average purchase price of shares across several transactions of different sizes, the average interest rate of a loan portfolio, or a product's average rating, where a review with a longer justification carries more weight. The weights don't have to add up to a hundred or to one. A weight can be a fraction, for example 0.5. An invalid line or a zero sum of weights ends with a clear message, not an empty result.
Frequently asked questions
How do you calculate the weighted average of grades 5 (weight 3), 4 (weight 2), and 3 (weight 1)?
The sum of products is 15 + 8 + 3 = 26, and the sum of weights is 6. The result is 26 divided by 6, which is 4.33. A plain average would give 4.0.
Do the weights have to add up to 100?
No. They can be any positive numbers — the calculator divides by their actual sum. Weights of 3, 2, 1 will give the same result as 30, 20, 10.
Can a weight be a fraction?
Yes. Values such as 0.5, 0,5, 1.25 or 1,25 are allowed. Separate the value from its weight with a space or semicolon.
What happens if I enter a weight of zero on every line?
The calculator will report an error, since division by zero makes no sense. At least one weight must be non-zero.
See also
Arithmetic Mean
Enter numbers separated by commas and calculate the arithmetic mean online. The calculator will give you the s
Combinations, variations and permutations
Calculate the number of combinations, variations and permutations of n elements taken k at a time. Combinatori
Geometric mean
Calculate the geometric mean of any number of values. The n-th root of the product. Useful for rates of return