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# For these data, calculate the standard deviation, . Round to the nearest tenths place...

lonestargirl56 | Student, Professional | Valedictorian

Posted May 26, 2013 at 10:29 PM via web

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For these data, calculate the standard deviation, . Round to the nearest tenths place if a fraction. The standard deviation is: Answer

A.

1.9

B.

2

C.

3.7

D.

3.8

E.

the standard deviation is a value not listed in alternatives "a" through "d"

llltkl | College Teacher | Valedictorian

Posted May 27, 2013 at 12:48 AM (Answer #2)

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We have the mean (`barx` ) = `(2+2+7+4+4+7+2+2+3)/9` = `33/9` = `11/3`

For calculation of variance,

`x_i`     `x_i-barx`      `(x_i-barx)^2`

`2`      `-5/3`      `25/9`

`2`    ` -5/3`     `25/9 `

`7 `     `10/3`     `100/9 `

`4`     `1/3`      `1/9`

`4`      `1/3`      `1/9`

`7`      `10/3`      `100/9`

`2`      `-5/3`     `25/9`

`2`      `-5/3`      `25/9`

`3`     `-2/3`      `4/9`

`Sigma(x_i-barx)^2 = 306/9 = 34`

Here, n=9 and `Sigma(x_i-barx)^2 = 34`

Hence Variance = `1/nSigma(x_i-barx)^2 = 34/9`

`rArr Standard Deviation = sqrt (Variance) = sqrt (34/9)`

`= sqrt34/3`

`= 1.9436506`

`= 1.9` (after rounding off to the nearest tenth place of a fraction)

Hence the correct answer is option A) 1.9

Sources:

lonestargirl56 | Student, Professional | Valedictorian

Posted May 26, 2013 at 10:31 PM (Answer #1)

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Here is the question:

The scores below are the number of
caffeinated beverages (coffee, tea, most carbonated
soft drinks)

that
9
consumed in a single day.

Scores:

2,

2,

7,

4,

4,

7,

2,

2,

3

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