Hi, I selected the wrong answer – option E – for the above question. I would like to better understand why the correct answer is option C, and what lapse in judgement I have made while eliminating it. Please see my thought process below.
Simplifying the paradox
During a week in 1987 the volume (number) of stocks traded (bought and sold) reduced. However, the total volume of stocks traded in 1987 remained similar to the previous year (1986).
Answering the question before looking at the answer choices
Volume of stocks traded in other weeks of 1987 must’ve been significantly higher than or similar to the average volume of the previous year.
Eliminating C
The phrase "that year" (1987) led me to eliminating answer choice C, because calculating average by definition means that during the year there were weeks where the volume remained equal to or greater than average, and does not indicate a comparison between the volumes of 1987 and 1986. In mathematical terms, let’s assume we have the following sets:
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Set A {1, 49, 50, 100}
** volume of A: 200
** average of A: 50 -
Set B {1, 2, 2, 3}
** volume of B: 8
** average of B: 2
You can see above for some portion of set B, the numbers (independent volumes) are greater than the average for that set (2). However, this does not provide any evidence that set A and set B have comparable volumes (200 vs 8).
Thus, I would be more convinced to choose option C if it was phrased: “For some portion of 1987, the volume of stocks traded was higher than the average for the previous year”.
Choosing E
Answer choices A, B, and D were fairly easy to eliminate for me. Even though Answer choice E goes against my outside knowledge of the stock market, all other answer choices had apparent flaws. E seemed the most probable since it best compares 1987 to the previous year, as it can be inferred that a predictable cycle would mean that volume of stocks remain fairly constant in the long term, and thus it’s rational that despite fluctuations in 1987, the total volume of stocks was not appreciably different from the preceding year’s volume.
Thank you for your answers in advance, I understand this is a cumbersome post, but this question has me truly baffled.