a boy measures the diameter of a small metal ball using a Vernier caliper he take the following five readings 2.48 2.49 2.51 2.15 M 2.51 cm find its radius with appropriate percentage
Answers
Given data,
2.48, 2.49, 2.51 ,2.15 and 2.51 .
No. of Observations = 5
∵ Mean = Sum of all Observations/No. of Observations
= (2.48 + 2.49 + 2.51 + 2.15 + 2.51 )/5= 12.14/5
= 2.428
Taking an approx value,
Mean = 2.43 [By taking an approximate value answer can be easily calculated]
For Calculating Absolute Error,
x₁ = |2.43 - 2.48| = 0.05
x₂ = |2.43 - 2.49| = 0.06
x₃ = |2.43 - 2.51| = 0.08
x₄ = |2.43 - 2.19| = 0.24
x₅ = |2.43 - 2.51| = 0.08
∴ Absolute Error(Δx) = (x₁ + x₂ + x₃ + x₄ + x₅)/5
= (0.05 + 0.06 + 0.08 + 0.24 + 0.08)/5
= 0.51/5 = 0.102
∵ Relative Error % = (Absolute Error/Mean Value) × 100 %
= (0.102/2.43) × 100 %
= 0.042 × 100%
= 4.2%.
∴ Relative Error % is 4.2 %.
There can be the little difference in the answer, because we have taken the approx mean value. But such difference can be neglected because it will be too hard calculations which will take lot of time.
In Examination also such differences are not considered.
Hope it helps.
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