Discussion
Pass percentage of a school for six consecutive years starting from 2003 to 2008 are 45, 56, 42, 61, 55 and 52. If the ratio of students who appeared for the exam in the years 2003 to 2008 are 2 : 3 : 4 : 3 : 2 : 3, then the pass percentage of the school in six years together is :
Answer: A
The overall pass percentage is 51.5%.
Because different numbers of students appeared each year, the yearly percentages must be weighted by the ratio of candidates, 2 : 3 : 4 : 3 : 2 : 3 (total 17 parts):
\[ \begin{aligned} &2(45) + 3(56) + 4(42) + 3(61) + 2(55) + 3(52) \\ &= 90 + 168 + 168 + 183 + 110 + 156 = 875 \\ &\frac{875}{17} \approx 51.47\% \approx 51.5\% \end{aligned} \]
The simple average of the six percentages, 311 / 6, is about 51.8%, close but not the right method, and it is not an option either. 47.5%, 55% and 42.5% come from no consistent weighting of the data.
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