Statistics: Median
$$Q$$ is a set of consecutive integers. Which of the following must be true?
>I) The sum of $$Q$$ is odd.
>II) The mean of $$Q$$ is an integer.
>III) The median of $$Q$$ is an integer.
Correct.
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I) If $$Q$$ has 4 elements (or any other number of elements that is a multiple of 4), such as $$\{1, \ 2, \ 3, \ 4\}$$, its sum is even (in this case, 10). Thus, option I doesn't _have_ to be true. __POE__ answer choice A.
II) If $$Q$$ has 4 elements (or any other even number of elements), such as $$\{1, \ 2, \ 3, \ 4\}$$, its mean is a fraction (in this case, 2.5). Thus, option II doesn't _have_ to be true. __POE__ answer choices B and D.
III) If $$Q$$ has 4 elements (or any other even number of elements), such as $$\{1, \ 2, \ 3, \ 4\}$$, its median is a fraction (in this case, 2.5). Thus, option III doesn't _have_ to be true. __POE__ answer choice C.
Therefore, answer choice E is the correct answer.
Incorrect.
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Incorrect.
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Incorrect.
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Incorrect.
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I only
II only
III only
II and III only
None of the above
