Without a unit of measurement, measuring is difficult. For example, what does it mean to "measure the quality of a text"? How should an exam paper be graded? Examiners generally tackle the problem by dividing the assessment into several components. An essay might thus have its mark split into four component marks, each worth five points: quality of expression (absence of errors, vocabulary, style), coherence (introduction, conclusion, transitions and links between sections), examples (choice, relevance, detail), and argumentation (clarity, precision, explanation). All examination and competitive-examination boards use criteria of this kind. Although the marks awarded by different members of a board often show some consistency, surprises are always possible. In such cases, measurement becomes subjective, however precise and sensible the marking scheme may be. Furthermore, it is easy to devise a marking scheme that produces a predetermined average. Even if the marks for each component could be determined entirely objectively, the weight assigned to each can be used to adjust the final marks.
Grade scaling in action ------------------------------
Let us consider an assignment divided into four equally weighted sections and completed by four candidates. The final marks are 9 for I (the average of 14, 10, 4 and 8), 7.5 for II, 10.5 for III and 13 for IV. How can we ensure that everyone receives at least 10 out of 20? There are several solutions. The simplest is known as the rubber-band rule. It consists in multiplying every mark by the same number. Here, the lowest mark (7.5) merely needs to become 10, which means multiplying by 4 / 3. The marks then become 12, 10, 14 and 17.33 respectively (rounded to 17 or 17.5, if preferred). This method has the drawback that it may produce marks above 20. To avoid that risk, we can look for other weightings… although this is not always possible.
Manipulations of this kind may cast doubt on whether everything can be measured. What probably matters is obtaining a ranking that remains unchanged whatever marking scheme is used. Unfortunately, even that is not always possible!