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Find the variance for the given data. Round your answer to one more decimal place than...

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sinoeforleh | (Level 1) Honors

Posted October 26, 2010 at 10:43 AM via web

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Find the variance for the given data. Round your answer to one more decimal place than the original data. 4,11,11, 2, and 8.

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krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted October 26, 2010 at 11:29 AM (Answer #1)

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The variance of any given set of data containing n values can be calculated as:

V = [(x1 - x)^2 + (x2 - x)^2 + (x3 - x)^2 + ...  (xn - x)^2]/n

Where:

x, x2, x3 ... xn represent the n values, and

x  = mean of n values = (x1 + x2 + x3 + ... +xn)/n

From the given values we calculate the mean x as:

x = (4 + 11 + 11 + 2 + 8)/5 = 36/5 = 7.2

And

(x1 - x)^2 = (4 - 7.2)^2 = 10.24

(x2 - x)^2 = (11 - 7.2)^2 = 14.44

(x3 - x)^2 = (11 - 7.2)^2 = 14.44

(x4 - x)^2 = (2 - 7.2)^2 = 27.04

(x5 - x)^2 = (8 - 7.2)^2 = 0.64

And

V = [(x1 - x)^2 + (x2 - x)^2 + (x3 - x)^2 + (x4 - x)^2 + (x5 - x)^2]/5

= 10.24 + 14.44 +143.44 + 27.04 + 0.64)/5

= 66.8

= 13.36

Rounding this off to 1 decimal place we get 13.4

Answer:

Variance = 13.4

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