3. The diameter of a given wire is measured by a screw
gauge.Six measurements of the diameter give the reading in cm
as :
0.035,0.036,0.038,0.034,0.037,0.036
a)What result would you quote about the diameter of the wire?
b)What is the mean absolute error for those measurements?
c)What is the percentage error of the experiment?
Answers
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Answer:
Observations are : 0.026 , 0.028, 0.027, 0.029 , 0.024, 0.027
Mean = sum of observations/number of observations
= (0.026 + 0.028 + 0.027 + 0.029 + 0.024 + 0.027)/6
= 0.0268 ≈ 0.027 cm
∴ mean value = 0.027 cm
Now, y₁ =|0.026 - 0.027| = 0.001
y₂ = |0.028 - 0.027| = 0.001
y₃ = |0.027 - 0.027| = 0.000
y₄ = |0.029 - 0.027| = 0.002
y₅ = |0.024 - 0.027| = 0.003
y₆ = |0.027 - 0.027| = 0.000
Now, absolue error ,∆y = (y₁ + y₂ + y₃ + y₄ + y₅ + y₆)/6
= (0.001 + 0.001 + 0.000 + 0.002 + 0.003 + 0.000)/6
= 0.007/6
= 0.00116
Now, relative error = absolute error/mean value
= 0.00116/0.027
= 0.04296
[Note:- answer may varies because mean value should take 0.0268cm .but for approximation I assume 0.027 cm. For better precision, plz take 0.0268cm ]