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A student determined the density of a solid to be 2.90, 2.91 and 2.93 gcm–3. If the...

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christiano-cr7 | (Level 1) Salutatorian

Posted June 20, 2013 at 4:58 PM via web

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A student determined the density of a solid to be 2.90, 2.91 and 2.93 gcm–3. If the actual density of this solid is2.70 gcm–3, how should the student'sresults be described?
(A)  high accuracy and high precision
(B)  low accuracy and high precision
(C)  high accuracy and low precision
(D)  low accuracy and low precision

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 20, 2013 at 5:38 PM (Answer #1)

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You need to determine the accuracy of the measurements using the following algorithm, such that:

- average the measurements

`M = (2.90+2.91+2.93)/3 => M = 2.913`

- subtract each measurement from average

`2.913 - 2.90 = 0.013`

`2.913 - 2.91 = 0.003`

`2.913 - 2.93 = -0.017`

- determine standard deviation

`sigma = (0.013 + 0.003 - 0.017)/3 = -0.001`

Since `sigma = -0.001` and the measurements differ from each other, the precision is low and the accuracy is high, hence, you need to select the option C.

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