the different measurements of length of a rod are 4.2 4.5 4.4 4.3 4.6cm calculate mean value absolute error mean absolute error fractional error percentage error solution step by step
Answers
Step-by-step explanation:
Mean = ( 4.2+4.5+4.4+4.3+4.6)/5
=
4.4 cm ( Ans)
Answer:
Mean = 4.4, Absolute error = 0.12, Fractional error = ± 0.027 and Percentage error = 2.7%
Step-by-step explanation:
Given:- The given values are 4.2, 4.5, 4.4, 4.3, 4.6
To Find:- Mean, Absolute error, Fractional error and Percentage error.
Solution:-
The given values are 4.2, 4.5, 4.4, 4.3, 4.6
Mean = sum of observation ÷ no. of observations
= (4.2 + 4.5 + 4.4 + 4.3 + 4.6) ÷ 5
= 22 ÷ 5
= 4.4
Absolute errors are:- Δx1 = 4.4 - 4.2 = 0.2
Δx2 = 4.4 - 4.5 = -0.1
Δx3 = 4.4 - 4.4 = 0.0
Δx4 = 4.4 - 4.3 = 0.1
Δx5 = 4.4 - 4.6 = -0.2
Mean absolute error = Sum of absolute errors ÷ no. of observations
= (0.2 + 0.1 + 0 + 0.1 + 0.2) ÷ 5
= 0.6 ÷ 5 = 0.12
Relative error or Fractional error = ± (absolute error ÷ mean )
= ± (0.12 ÷ 4.4)
= ± 0.027
Percentage error = Relative error × 100
= ± 0.027 × 100
= 2.7%
Therefore, Mean = 4.4, Absolute error = 0.12, Fractional error = ± 0.027 and Percentage error = 2.7%
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