From the information below determine the standard deviation:

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

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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

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`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**.

**Sources:**

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