Statistics: Standard Deviation
A certain set of numbers has an average (arithmetic mean) of 10 and
a standard deviation of 2.5. If $$X$$, a number in the set, is within two
standard deviations from the average, then which of the following
_cannot_ be the value of $$X$$?
Correct.
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If the standard deviation is 2.5, then two standard deviations equal 5. The variable $$X$$ can therefore be higher or lower than the mean by up to 5, which is anywhere between
>$$10 - 5 = \color{blue}{5}$$ and $$10 + 5 = \color{blue}{15}$$.
The number 2 is the only number in the answers that is not within that range.
Incorrect.
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2
5.5
6
10
14
