When the eleven plus examinations are marked the mark on each paper does not simply sit there waiting for something to happen. It is gathered up into a frequency distribution. This is essentially a table showing the marks each candidate is given.
If there are eighty questions on a paper the examiner marks the master paper from 80 to 1. The examiner then makes a tally for each candidate who has obtained the mark. For convenience sake every fifth tally is crossed across the preceding four to make a gate. Each gate is worth five tallies.
The total number of tallies should be equal to the total number of scripts.
Years ago conscientious school masters, school mistresses and clerks would have calculated the tallies and found the mean or average. The average is not really the average mark – but is the arithmetic mean.
Today the whole operation must be carried out by computer. This must reduce the kind of errors than may have crept in years ago.
In some verbal reasoning tests the examiners try to increase the effectiveness of the examination by throwing a large number of questions at the children. It is no good, however, making the questions too hard because then few children would benefit. The examiners also have the weapon of speed.
Every parent has said, sometimes rather plaintively, “If the question is too hard, then leave it, and go on to the next question.”
If an eleven plus examination is too easy then a bulge of correct answers would appear at the bottom of the table. In theory the examiners are trying to have half the questions answered correctly. They can then set the pass mark where ever they want – because to all intents and purposes the actual test has been as fair as possible. The pass mark can then be adjusted to take into account the number of places in the grammar schools.
One school can then set a pass mark higher or lower than another school.