Statistics: Median
$$v$$, $$w$$, $$x$$, $$y$$, and $$z$$ are five positive integers for which $$v\le w\le x\le y\le z$$. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, what is the smallest possible value of $$z$$?
Incorrect.
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Correct.
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If $$v=w=x=25$$, their sum is 75. Since, the sum of all five numbers is 150, the sum of $$y$$ and $$z$$ must be $$150-75 = 75$$. To make $$z$$ as small as possible, divide 75 evenly between $$y$$ and $$z$$. Since you get 37.5, and $$y$$ and $$z$$ must be integers, then $$y = 37$$ and $$z = 38$$.
Incorrect.
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Incorrect.
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Incorrect.
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30
35
37
38
40
