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24 Jun 2024, 09:10
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Question Stats:
100% (01:00) correct
0% (00:00) wrong based on 2 sessions
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In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.
Quantity A
The median of the 24 integers
Quantity B
50
Quantity A
The median of the 24 integers
Quantity B
50
14 Jul 2024, 11:31
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Official Explanation
In general, the median of a set of n positive integers, where n is even, is obtained by ordering the integers from least to greatest and then calculating the average (arithmetic mean) of the two middle integers. For this set of 24 integers, you do not know the values of the two middle integers; you know only that half of the integers are less than 50 and the other half are greater than 50. If the two middle integers in the list are 49 and 51, the median is 50; and if the two middle integers are 49 and 53, the median is 51. Thus the relationship cannot be determined from the information given, and the correct answer is Choice D.
In general, the median of a set of n positive integers, where n is even, is obtained by ordering the integers from least to greatest and then calculating the average (arithmetic mean) of the two middle integers. For this set of 24 integers, you do not know the values of the two middle integers; you know only that half of the integers are less than 50 and the other half are greater than 50. If the two middle integers in the list are 49 and 51, the median is 50; and if the two middle integers are 49 and 53, the median is 51. Thus the relationship cannot be determined from the information given, and the correct answer is Choice D.
