Calculating the average of percentages from fields which have a "weight" multiplier applied.

Question

This is for some software I'm writing.

I have a number of fields, all of which have a score input which allows a percentage of 0-100. Each field has a "weight" property, which determines its significance, and should affect the overall calculated average of all the fields.

Example:

Field    |  Weight  |  Score %
--------------------------------
A        |  1.0     |  30
B        |  2.0     |  57
C        |  3.5     |  84
D        |  1.0     |  91
E        |  2.0     |  77
F        |  4.0     |  12

The normal average of the scores would be 58.5 but the weight of each field should be applied to proportionally influence the average.

• Field B's score should be twice as important as Field A
• Field F's score should be four times as important as Field A
• etc.

I would appreciate any explanation / pseudo-maths as to the most efficient way to approach this, and I will apply it to my software as appropriate.

If somebody could please tag this post appropriately - I'm not sure what to tag it with.

Answer 1

The weighted average of a set of $N$ numbers $x_k$ (in your case, the scores) where each number has weight $w_k$ is simply $$ \bar{x} = \frac{w_1x_1 + w_2x_2 + w_3x_3 + \ldots + w_Nx_N}{w_1 + w_2 + w_3 + \ldots + w_N} = \frac{\sum_{k\,=\,1}^{N} w_kx_k}{\sum_{k\,=\,1}^{N} w_k} $$

In words, you multiply each score by its corresponding weight, then sum all of those values, then divide that result by the sum of the weights. You can do both sums in a single loop then do the final division after the loop ends.

In pseudo-code, it looks like this:

• num = 0 // num stands for the numerator
• den = 0 // den stands for the denominator
• for k = 1 to N do
  • num += w[k] * score[k]
  • den += w[k]
• avg = num / den // avg stands for the weighted average