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From the information below determine the standard deviation: 1754, 1633, 1502, 1476,...

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yaga49 | Valedictorian

Posted June 18, 2013 at 1:49 PM via web

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From the information below determine the standard deviation:

1754, 1633, 1502, 1476, 1846, and 1478

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llltkl | College Teacher | Valedictorian

Posted June 18, 2013 at 2:24 PM (Answer #1)

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We have

Mean, `stackrel(-)(x)` = (1754+1633+1502+1476+1846+1478)/6 = 1614.833

Calculation of Variance:

`x_i`               `x_i -stackrel(-)(x)`             `(x_i -stackrel(-)(x))^2`

 1754       139.1667            19367.36

1633        18.1667              330.0278

1502        -112.833            12731.36

1476        -138.833            19274.69

1846         231.1667          53438.03

1478        -136.833           18723.36

---------------------------------------------                                

                                `sum(x_i-stackrel(-)(x))^2` = 123864.8

Here n = 6    

Therefore, Variance =  `1/n sum(x_i-stackrel(-)(x))^2`

= 123864.8/6

= 20644.14

`rArr` Standard Deviation = `sqrt(Variance)`

= `sqrt(20644.14)`

= `143.6807` .

Therefore, the Standard Deviation of the given set of data is 143.6807.

139.1667 18.16667 -112.833 -138.833 231.1667 -136.833

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