WORLD OF FIGURES: How did top students get identical marks in all subjects?

A curious observation was made soon after the release of the Kenya Certificate of Primary Education (KCPE) examinations results.

The top place was tied between two pupils — Rawlings Odhiambo and Olive Mwea — and both scored exactly the same marks in each of the five subjects: Mathematics — 99 per cent, English — 92, Kiswahili — 97, Science — 81 and Social Studies — 84.

Several people claimed that this is statistically impossible, but the truth is that it is possible. In principle, statistics deal with the probability of an outcome in a very simple way.

All you do is ask how many outcomes can occur. Then, the probability of one of them occurring is simply one divided by the total number of possible outcomes.

So what is the probability that two pupils, a boy and a girl, will score exactly the same marks in each and every subject at KCPE? Without doing any calculations, we can say that it is very small, but it is not zero!

In fact, it is exactly the same as scoring any other specific combination of marks.

Say, for example, Rawlings scoring 98, 94, 96, 82, and 83; while Olive gets 97, 93, 95, 83, and 85. The probability is this specific outcome is exactly the same as the probability of them getting identical marks!

THE STANDARDIZATION PROCESS

But there is another side to this story: the mathematics and science papers have 50 multiple-choice questions each. Therefore, the percentage marks should always be an even number.

How come these two pupils were awarded odd marks in these subjects: Mathematics — 99 and Science — 81? The answer lies in the process of standardisation of results.

KCPE results are standardised to ensure that the national average score in each subject is 50 and the spread of marks (standard deviation) is +/- 15.

I explained how this is done in March 2015; the end result in most years is that the very high scores are reduced while the very low ones are increased. It is not a secret and it is not a Kenyan peculiarity!

I am surprised nobody finds it strange that out of one million candidates, no one scored 100 per cent in any single subject! Our brightest pupils could only manage 99 per cent at best.

I am quite sure that many scored 100 per cent in various papers but the standardisation process reduced their final scores. I suspect that this is what happened to the two top candidates.

They got all the answers correct in the multiple-choice questions and scored the highest possible marks in the English and Kiswahili essays. That is not unexpected, after all, these are the best students out of one million!

At that point, their marks in each subject were identical — 100 per cent all through.

The standardisation process for each subject is done separately. Therefore, an initial 100 per cent in mathematics will come out as a different figure from an original 100 per cent in science.

www.figures.co.ke; Twitter: @MungaiKihanya