# From the information below determine the standard deviation: 1754, 1633, 1502, 1476, 1846, and 1478

llltkl | College Teacher | (Level 3) Valedictorian

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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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