The observation value for an experiment is given as 1.42, 1.43, 1.45, 1.41, 1.49. Calculate its absolute error, arithmetic mean error, relative error, percentage error.

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Solution

Dear Student,

$1.42, 1.43, 1.45, 1.41, 1.49 a b s o l u t e v a l u e a = \frac{1.42 + 1.43 + 1.45 + 1.41 + 1.49}{5} = 1.44 a b s o l u t e e r r o r i n a l l t h e v a l u e s ∆ a 1 = |1.44 - 1.42| = 0.02 ∆ a 2 = |1.44 - 1.43| = 0.01 ∆ a 3 = |1.44 - 1.45| = 0.01 ∆ a 4 = |1.44 - 1.41| = 0.03 ∆ a 5 = |1.44 - 1.49| = 0.05 m e a n a b s o l u t e e r r o r ∆ a_{m} = \frac{0.02 + 0.01 + 0.01 + 0.03 + 0.05}{5} = 0.024 r e l a t i v e e r r o r = \frac{∆ a_{m}}{a} = 0.017 p e r c e n t a g e e r r o r = 0.017 * 100 = 1.7 p e r c e n t . R e g a r d s$

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