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10 Feb 2020, 23:03
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A
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Difficulty:
25%
(medium)
Question Stats:
73% (01:23) correct
27%
(01:16)
wrong
based on 64
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In a survey report, each surveyed man was assigned a gender code of 1 and each surveyed woman was assigned a gender code of 0. If 100 people were surveyed, were more men surveyed than women?
(1) The median of all the gender codes noted in the survey report was 1.
(2) The average (arithmetic mean) of all the gender codes noted in the survey report was less than 0.6
(1) The median of all the gender codes noted in the survey report was 1.
(2) The average (arithmetic mean) of all the gender codes noted in the survey report was less than 0.6
15 Feb 2020, 02:23
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Can someone explain this?
16 Feb 2020, 09:22
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Assuming all 100 codes were assigned as described, we have a list of 100 values, and every value is either "0" or "1".
To find the median of that list, we would need to list the values in increasing order, and average the 50th and 51st highest values. Those must each equal 0 or 1, since those are the only values we have. If the median is "1", they both must equal 1. But that means the 51st highest value in the set is 1, so we have at least 51 "1"s and at most 49 "0"s, and therefore more men than women.
If the average of 100 values is less than 0.6, the sum of the 100 values is less than 60 (because avg = sum/n). Since the only values contributing to our sum are the "1"s, Statement 2 tells us we have less than 60 "1"s in our set. We might have, say, 55 of them, and have more men than women, or we might have 45 of them and have more women than men. So Statement 2 is not sufficient and the answer is A.
To find the median of that list, we would need to list the values in increasing order, and average the 50th and 51st highest values. Those must each equal 0 or 1, since those are the only values we have. If the median is "1", they both must equal 1. But that means the 51st highest value in the set is 1, so we have at least 51 "1"s and at most 49 "0"s, and therefore more men than women.
If the average of 100 values is less than 0.6, the sum of the 100 values is less than 60 (because avg = sum/n). Since the only values contributing to our sum are the "1"s, Statement 2 tells us we have less than 60 "1"s in our set. We might have, say, 55 of them, and have more men than women, or we might have 45 of them and have more women than men. So Statement 2 is not sufficient and the answer is A.
