Question

The values for the diameter of wire as measure by screw gauge were found to be 0.026

Answer 1

plz give complete information.
well, A complete question may be -----> The values for the diameter of a wire as measured by a screw gauge were found to be 0.026cm, 0.028cm, 0.027 cm,0.029cm,0.024cm, 0.027cm find the mean value and relative error?

solution :- 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 ]