Weighted average calculator

What it's for

The weighted average gives more importance to values with a higher weight (for example exams with more credits). Different from the simple average, which treats everything equally.

How to write it

One line per item: first the grade, a space, then the weight (credits, hours, coefficient). Example: «28 9».

When a simple average misleads

A simple average treats every entry the same way, and that only works when they really do weigh the same. A 12-credit exam and a 3-credit one don't weigh the same: the first took four times as long, and counts four times in the record. Anyone working out the simple average of their marks nearly always gives themselves a number higher than the real one, because the small exams, which are the easiest to score high on, count like the big ones.

The same holds outside university: the final mark of a course where the exam is worth 70% and coursework 30%, the average of an investment made in two payments of different size, the mean rating of a product with reviews collected over different periods.

How it's worked out

You multiply each value by its weight, add up all the products, and divide by the sum of the weights — not by the number of entries, which is the classic mistake. With 28 on 9 credits and 24 on 6: (28×9 + 24×6) ÷ (9+6) = 396 ÷ 15 = 26.4. The simple average would have said 26, and the gap grows when the weights differ a lot.

The weights don't have to be credits: hours, percentages, numbers of items, anything expressing relative importance will do. And they don't have to add up to a hundred: they get divided by their own sum anyway, so «3 and 1» works like «75% and 25%».

Nearby tools

For the simple average and the other statistics of a list there is Sum a list of numbers. To find out what mark you need in the next exam to reach a target average the page is What mark do I need, and to compare marks on different scales Grade converter.