Weighting is a means of attributing relative importance to different components of a test or examination.
Example one
In a GCSE examination which has three components - A, B and C - the raw marks for component A are weighted twice as much as the raw marks for component B, and those for component C are weighted half as much as the raw marks for component B. Thus, marks for A would be doubled and those for C halved before totalling, giving the formula:
Final mark = (2 x A) + B + 
C
Example two
A pupil achieved the following marks in tests A, B and C.
| Test |
A |
B |
C |
|---|
| Raw mark |
68 |
28 |
5 |
|---|
The pupil's weighted score was calculated using the following formula:
| Weighted score = |
(A x 60)
100 |
+ |
(B x 30)
80 |
+C |
|---|
What was the pupil's weighted score? Give your answer to the nearest whole number.
| Weighted score |
= |
68 x 60
100 |
+ |
28 x 30
80 |
+5 |
|---|
|
= 40.8 + 10.5 + 5 = 56.3 |
|---|
Example three
A GCSE examination consists of two papers. Paper 1 has a maximum raw mark of 40 and a final weighting of 30%. Paper 2 has a maximum raw mark of 160 and a final weighting of 70%, as shown in the table.
| Maximum raw mark | Weighting % |
| Paper 1 |
40 |
30 |
|---|
| Paper 2 |
160 |
70 |
|---|
Find the final weighted mark for a pupil who gained 27 marks in paper 1 and 93 marks on paper 2.
For paper 1: the score of 27 out of 40 is equivalent to a weighted percentage of
x 30% = 20.25%, ie 20.3%
For paper 2: the score of 93 out of 160 is equivalent to a weighted percentage of
x 70% =" 40.68%, ie 40.7%
So the final weighted mark is 20.3% + 40.7% = 61%