By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

08 March 2015

Last week I demonstrated that the minimum score any candidate should get in the Kenya Certificate of Primary Education is 99 out of 500. Having done that calculation, I suggested that a student can score pretty good marks if he only knows half of the subject matter.

Such a student would answer half the questions correctly and guess the remaining half. That way, he would score 61 per cent in Mathematics and science respectively, and 62 per cent in Social Studies. I leave for you to confirm those numbers!

In the language papers, he would get 31 out of 50 in the objective questions and, perhaps 15 out of 40 in the compositions. This would bring the overall score in each paper to 51 per cent.

So, the total score for a student who knows only half the subject matter comes to 61 + 61 + 62 + 51 + 51 = 286. This is a strong C+ grade, which is a pretty good performance!

If it is so easy to pass, how comes some candidates end up with marks below the academic minimum of 99 out of 500? The answer lies in a process known as normalisation, or standardisation of marks.

It is not a secret! The Kenya National Examinations Council publishes this information every year in its annual KCPE report which is available in the bookshops at a small cost. In addition, it is not a Kenyan peculiarity to normalise results: it is a common practice the world over.

The objective of this normalisation is to ensure that the scores in each subject fall on a normal distribution curve with the national mean of 50 out of 100 and an average scatter of plus or minus 15. That is, the majority of the candidates (68 percent) get between 35 and 65 marks.

The normalised / standardised score, S, for a candidate is calculated using this formula:  S = 50 + 15x(R – M)/d; where R is the raw marks scored by the candidate, M is the national average for the subject and d is the national average scatter of marks (standard deviation).

Suppose the national mean in an exam paper is 20 and the standard deviation is 10; the standardised score of a student whose raw marks are 25 works out as follows:

S = 50 + 15x(25 – 20)/10 = 50 + 15x5/10 = 50 + 75/10 = 57.5. This is a whole 32.5 marks above the actual score.

On the other hand, for a candidate whose raw score is 15, the standardised marks are: S = 50 + 15x(15 – 20)/10 = 50 – 15x5/10 = 50 – 75/10 = 42.5. This is 27.5 marks above the actual score.

Now consider a very poor candidate in a fair exam where the national average score is 45 with a standard deviation of 10. If his raw marks are 25, the standardised score comes to:

S = 50 + 15x(25 – 45)/10 = 50 – 15x20/10 = 50 – 30 = 20. That is, the standardised score is LOWER than his raw marks! This is how some candidates end up with marks below what I called the absolute academic minimum.