Calculate Weighted Sum
Calculator for the weighted sum with the sum symbol Sigma, Σ. The weighted sum is a sum in which each summand receives a multiplier, the weight. Please enter a sum term and the weights. If there are fewer weights than steps, the weights start again from the beginning. The weights must be numbers separated by ; or by spaces. The sum term can contain the same expressions as the sum calculator. As weights, only numbers and separators are allowed.
As an example of weighting, a very simple sequence of numbers is chosen here: 1 2 3. This sequence repeats until all steps of the sum have been completed, i.e., 1 2 3 1 2 3 1, and so on. The default formula behind the summation symbol, i, is also very simple. It causes the numbers from 1 to 100 to be added consecutively. The weighting has the effect that instead of calculating 1+2+3+4+5+6+7..., the calculation becomes 1+4+9+4+10+18+7...
The sum of the numbers from 1 to 100 is 5050. This is known from an anecdote about the young Carl Friedrich Gauss, who calculated 1+100, 2+99, and so on, i.e., 50*101, thus discovering a summation formula while still in school. With weighting, such a conversion becomes more complicated. Since the average of 1, 2, and 3 is 2, it can be quickly estimated that the weighted sum is about twice as large. The final result, 10066, is slightly smaller because the last value is 1, which therefore occurs one more time than 2 and 3.
Additional calculation results are the sum of the weights and the weighted mean. The sum of the weights can probably be ignored in most cases. The weighted mean is the arithmetic mean of the weighted values, which is simply the final result divided by the number of steps. Mean values are frequently needed.
