


arithmetic mean of x and y 


geometric mean of x and y 


harmonic mean of x and y 


Examples (to nearest whole percent)
x  y  arithmetic mean  geometric mean  harmonic mean 
50  50  50  50  50 
40  60  50  49  48 
30  70  50  46  42 
20  80  50  40  32 
Geometric means of an exam mark of x with an assignment mark of 100x 
Harmonic means of an exam mark of x with an assignment mark of100x 
Notice that the arithmetic mean is in all cases 50.
Clearly the geometric and harmonic means penalise uneven performances, but the harmonic mean penalises them more heavily. Reasons that lecturers might wish to do this include (1) preventing students, who have obtained high marks on the assignments by undetected plagiarism, from passing or doing well: such students are unlikely to do well in the exam, and (2) preventing students who cannot succeed at the programming assignments, but who are good at the theory, or at exam technique, or at memorising facts, from passing or doing well. By doing this, lecturers are maintaining the standard of the qualification towards which you are working. If students who cheat, or who cannot program, get through School of CSE degrees, eventually the word will spread to employers, and the value of your qualification will decline.








Examples (to nearest whole percent)
x  y  weighted arithmetic mean  weighted geometric mean  weighted harmonic mean 
80  20  62  53  42 
70  30  58  54  50 
60  40  54  53  52 
50  50  50  50  50 
40  60  46  45  44 
30  70  42  37  36 
20  80  38  30  26 
Weighted geometric means of an exam mark of x with an assignment mark of 100x. Weighting is 70% for exam, 30% for assignments. 
Weighted harmonic means of an exam mark of x with an assignment mark of 100x. Weighting is 70% for exam, 30% for assignments. 
Further variations are possible, but rarer in practice. They include means, weighted or not, of more than two marks. For example, a lecturer might weight exam, midsession quiz, and assignments as 50%, 20% and 30%, and then combine those marks using a harmonic mean formula.
© Bill Wilson, 2006
UNSW CRICOS Provider No.: 00098G
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