Calculation of averages

Calculation of Averages

Every term, students are tested a number of times on every subject and the different test results are used to calculate averages for the different subjects.  These averages reflect student performance in the different subjects, higher averages indicating better performance.

Most schools use simple arithmetic averaging methods, such that a student who gets in a certain subject a 40% on one test, a 60% on the second, and an 80% on the third, gets an average of  (40%+60%+80%)/3 = 180%/3 = 60%. Another student whose average for the same subject over the same interval is 70%, for example, is considered to have done better than the previously mentioned student.

Now let us consider two students St 1 and St 2 who take three tests, the first on September 10, the second on October 10 and the third on November 9.  If St 1 got 40% in the first test, 60% in the second, and 80% in the third, then it is clear that that student has improved their marks over the term.  If on the other hand, St 2 during the same term in the same subject got 80% in the first exam, then 60% in the second, and then 40% in the third, then the second student has regressed over the term.  Schools in general grant both students the same average of 60%, because (40%+60%+80%)/3 = (80%+60%+40%)/3 = 60%.  But how can we give these two students equal averages and at the same time claim that we encourage progress.

We also question the validity of assuming that a mark of 80% achieved a year ago is of the same importance as one which had been achieved only yesterday.  Recent information, if all other variables are fixed, is more reliable than old information because with time the value of knowledge, like everything else, fades away.

Student progress should be encouraged and rewarded, and recent marks must be considered of higher importance than older ones.  The two above students hence must not be awarded equal averages. For that purpose, we at EDUGATES have introduced a time factor for calculating averages allowing for the required differentiation.

We are not the only educational group who consider that older marks are of less value; we all know that almost all international standardized examinations marks expire after a couple of years.

To reflect the trend of the results when we calculate the average of St 1 and St 2, we need to give an earlier test a lower weight than a more recent one.  We have therefore introduced a formula that makes the weight decrease with time from 1.0 to 0.5.

Assume that the period of evaluation of the students mentioned above starts on September 1 and ends on December 16.  The third row of the table below shows the weights of the different tests in a report which is produced on December 16.  Weights are calculated according to the following formula:

Weight = 1 – (number of days between the date of the exam and the date of the report)/2(number of days of the term).  In the last column of the table you can see that the averages of the two students now differ slightly, to the advantage of the one who has improved with time.

We realize that our representation of student performance is innovative and hence is going to invite controversy. However, we feel that it is our duty as educators to think of the impact of our decisions on students.  Even though slight in the example below, we believe the difference in average is important.

Test	T1	T2	T3	Term Start: Sep 1
Date	Sept 10	Oct 10	Nov 9	Term End: Dec 16
Weight	0.55	0.69	0.83	Average
S1	40	60	80	62.72
S2	80	60	40	57.28

Parents, administrators, and teachers who wish to verify averages, are kindly requested to use the above method in their calculation.