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  • Time interval mesured by a clock give the following readings: 1.21 s,1.25 s, 1.24 s, 1.27 s, and 1.28 s. What is the percentage relative error of the observation ?<div class='qna-opti

Time interval mesured by a clock give the following readings:

1.21 s,1.25 s, 1.24 s, 1.27 s, and 1.28 s. What is the percentage relative error of the observation ?

Option: 1

4 %


Option: 2

16%


Option: 3

1.6%


Option: 4

2%


Answers (1)

best_answer

Given,

t1 = 1.25s

t2 = 1.24s

t3 = 1.27s

t_{4} = 1.28s

\small t_{5}=1.21s
\small t_{mean}=\frac{t_{1}+t_{2}+t_{3}+t_{4}+t_{5}}{5}

\small t_{mean}=\frac{1.25+1.24+1.27+1.28+1.21}{5}=1.25

\small E_{1}=1.25-1.25=0\\E_{2}=1.25-1.24=0.01\\E_{3}=1.25-1.27=-0.02\\E_{4}=1.25-1.28=-0.03\\E_{1}=1.25-1.21=0.04

 

\text{Relative Error}=\frac{\text{Sum of Absolute error }}{\text{Mean value}\times n}\times 100%

\small =\frac{|E_{1}|+|E_{2}|+|E_{3}|+|E_{4}|+|E_{5}|}{1.25\times 5}\times 100%

\small =\frac{0+0.01+0.02+0.03+0.04}{1.25\times 5}\times 100%

\small =1.6%

 

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vinayak

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