Why divide by the total weight?

Because the weights say how many times each value effectively counts. Dividing by the number of items instead gives a figure that is neither the weighted nor the simple average.

What do I need on the final assessment?

Enter your target and the weight still to come. The page solves for the score required, and says when the target has become unreachable.

Math & Statisticsstatistics

Weighted Average Calculator

Weighted average with each item's contribution, and what a remaining item needs to score to hit a target. The gap against the simple average shows how much the weighting is doing.

Also called: weighted mean calculator, weighted grade calculator.

Weighted average

86.3

86.3 against a simple average of 83.75, a difference of 2.55. The heaviest item is 88 at 40% of the total weight, which is why the weighted figure sits above the simple one. Enter a target and the weight still to come to see what the remainder has to score.

Simple average

83.75

Difference from the simple average

2.55

Total weight

Weighted sum

863

Value carrying the most weight

Share of the total weight

40%

Score needed on what remains

On the weighting

The heaviest item is 88 at 40% of the total weight, which is why the weighted figure sits above the simple one.

On the target

Enter a target and the weight still to come to see what the remainder has to score.

How this is calculated

Method and background

How this is calculated

Multiply each value by its weight, sum, and divide by the total weight rather than the count. That last step is what people forget: dividing by the number of items instead of the total weight gives a number that is neither average. Comparing against the simple mean shows whether the weighting matters at all, and where a target is given the page solves for what the remaining weight has to score, which is the usual reason for computing this mid-course.

dividing by the total weight rather than the count is what separates this from a simple mean

w: Weights
x: Values

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

four values with weights

Values: 80, 92, 75, 88
Weights: 2, 3, 1, 4
Target average, if you have one: 0
Weight still to come: 0

Weighted average86.3

863 over a total weight of 10, against a simple mean of 335 over 4

Open this example

solving for what a final assessment needs

Values: 80, 92, 75, 88
Weights: 2, 3, 1, 4
Target average, if you have one: 88
Weight still to come: 5

Weighted average86.3

boundary: 88 times 15 less the 863 already earned, over the remaining 5

Open this example

Method and limits

What it assumes

Values and weights paired in order, with equal counts.

What it deliberately does not model

Weights of zero remove an item entirely rather than giving it no influence, which is the same thing here but not in every scheme.
A target may be unreachable with the weight remaining, which the page says rather than returning an impossible score.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Why divide by the total weight?: Because the weights say how many times each value effectively counts. Dividing by the number of items instead gives a figure that is neither the weighted nor the simple average.
What do I need on the final assessment?: Enter your target and the weight still to come. The page solves for the score required, and says when the target has become unreachable.