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 100-x |
Harmonic means of an exam mark of x
with an assignment mark of100-x |
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 | 39 | 36 |
20 | 80 | 38 | 30 | 26 |
Weighted geometric means of an exam mark of x
with an assignment mark of 100-x. Weighting is 70% for exam, 30% for assignments. |
Weighted harmonic means of an exam mark of x
with an assignment mark of 100-x. 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, mid-session 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
Last updated: