What is the standard deviation of {4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}?

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What is the standard deviation of {4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}?

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Answer 1 · 2016-02-21T10:19:49

Standard Deviation is 2.2913

Explanation:

Set of numbers are ${4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}$ ${4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}$ . As there are 12 terms whose sum is 54, mean is $\frac{54}{12}$ $54/12$ or $4.5$ $4.5$ .

Hence deviations from mean are ${- 0.5, 0.5, 3.5, - 1.5, 1.5, - 2.5, - 3.5, 0.5, 4.5, 0.5, - 0.5, - 2.5}$ ${-0.5, 0.5, 3.5, -1.5, 1.5, -2.5, -3.5, 0.5, 4.5, 0.5, -0.5, -2.5}$ and sum of there squares is

$0.25 + 0.25 + 12.25 + 2.25 + 2.25 + 6.25 + 12.25 + 0.25 + 20.25 + 0.25 + 0.25 + 6.25 = 63$ $0.25+0.25+12.25+2.25+2.25+6.25+12.25+0.25+20.25+0.25+0.25+6.25=63$

Hence Standard Deviation is $\sqrt{\frac{63}{12}} = \sqrt{\frac{21}{4}} = \frac{1}{2} \sqrt{21} = \frac{4.5826}{2}$ $sqrt(63/12)=sqrt(21/4)=1/2sqrt21=4.5826/2$ i.e. $2.2913$ $2.2913$

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What is the standard deviation of {4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}?

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