Discussion
In a class of 50 students, the average marks in an examination was 48. However, after scrutiny, it was found that one student who scored 67 was awarded 37 by mistake, and another student who scored 73, was also awarded 37 by mistake. What should have been the actual average marks in that examination ?
Answer: B
The actual average should have been 49.32.
The total of the recorded marks was 50 × 48 = 2400. The two mistakes understated the total by (67 - 37) + (73 - 37) = 30 + 36 = 66 marks.
\[ \begin{aligned} \text{correct total} &= 2400 + 66 = 2466 \\ \text{average} &= 2466 / 50 = 49.32 \end{aligned} \]
A quicker route: the average rises by 66/50 = 1.32, from 48 to 49.32. 46.68 is what you get by subtracting the correction instead of adding it, and 51.60 and 50.66 do not match the correction of 66 marks.
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