# Statistics: Standard Deviation

$$M$$ is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 2.5. $$Q$$ is a subset of $$M$$ consisting of five terms. Exactly 80% of the numbers in $$Q$$ are located within two standard deviations from the average of $$M$$. Which of the following could $$Q$$ be?
Incorrect. [[snippet]] All five numbers are within the wanted range, so $$\frac{5}{5} = 100\%$$ are within two standard deviations from the mean, which violates the requirement that exactly 80% of $$Q$$ are within that range.
Incorrect. [[snippet]] Both 1 and 18 are not in the wanted range. Thus, only $$\frac{3}{5}=60\%$$ are within two standard deviations from the mean.
Incorrect. [[snippet]] The numbers 3 and 16 are not in the wanted range. Thus, only $$\frac{3}{5} = 60\%$$ are within two standard deviations from the mean.
Correct. [[snippet]] The numbers 6, 7, 10, and 12 are all within the wanted range of 5 to 15, but then number 3 is not. Thus, $$\frac{4}{5} = 80\%$$ of the numbers are within two standard deviations from the mean, as required.
Incorrect. [[snippet]] The numbers 3 and 4 are not in the wanted range. Thus, only $$\frac{3}{5} = 60\%$$ are within two standard deviations from the mean.
$$\{3, \ 4, \ 5, \ 10, \ 14\}$$
$$\{3, \ 6, \ 7, \ 10, \ 12\}$$
$$\{3, \ 5, \ 5, \ 10, \ 16\}$$
$$\{1, \ 5, \ 7, \ 10, \ 18\}$$
$$\{5, \ 6, \ 7, \ 10, \ 12\}$$

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