Exam results were correct, that is why failures are complaining
12 months ago, 11 Jan 22:20
Nothing in this universe is truly random. If you look at it from above, below, sideways and inside out, a pattern will begin to emerge. There is a predictable description for a lot of the stuff even in the social world. For example, if you step outside with a tape measure and you take the height of 100,000 people and plot the height scores on the x axis and your subjects on the y axis, you will discover that 68 per cent of them are of average height (34 per cent slightly below average and 34 per cent slightly above average), 13 per cent will be tall, 2.1 per cent will be remarkably tall and 0.1 per cent will be way too tall. In the other direction, 13 per cent will be short, 2.1 per cent will be very short but only 0.1 per cent will be laptop-sized. This is because height, just like IQ test scores and examination results, follow a statistical rule called normal distribution or the bell curve. I went back to read up on this and it is amazing how much of the awful stuff from nightmarish statistics units I have forgotten. STANDARD DEVIATION Student’s t-test? What the hell is all that? However, something useful stuck in some unused corner of my mind (there could be several of those). I recalled that the scores of the majority of students who sit an exam should be one standard deviation from the mean. Draw a long line on the ground and call it Y, mark its beginning on the left F and its end on the right A. At F, draw a vertical line and call it X. So that we aren’t here till tomorrow, forget X. Next, draw an inverted bell on Y, ensuring that it has a long tail tending towards F, but never touching Y and tending by the same distance towards A. Draw a line from the mid-point of the bell’s hump to intersect Y at the dead centre between F and A. Call the point of intersection C. That line is your mean. Starting from C, take one step towards A and mark that point C1. Go back to C and towards F, take a similar step and mark it C2. Think of that step as one standard deviation from C, our mean. The rule is that 68 per cent of students who take a test will have scores one standard deviation from the mean, that acreage between C1 and C2. INTELLIGENCE I am determined not to get lost in this but suffice it to say that, in measures of intelligence, the majority must get an average score. Similarly, in an exam, all factors being constant, a majority of the students should get a good, average mark, a few bright ones will get As, a few exceptional ones will dance for the cameras and a few challenged ones will not get much. The reason I have gone to the trouble of digging up ...
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