# Time intervals measured by a clock give the following readings: 1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s

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Time intervals measured by a clock give the following readings:

1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s

What is the percentage relative error of the observations?

(1) 1.6%

(2) 2%

(3) 4%

(4) 16%

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Ans: (1) 1.6%

Sol. The arithmetic mean of given values is taken as true value.

$t_{mean}={t_1+t_2+t_3+t_4+t_5\over5}$

$t_{mean}={1.25+1.24+1.27+1.21+1.28\over5}$

$t_{mean}=1.25 s$

$\Delta t_{mean}={|\Delta t_1|+|\Delta t_2|+|\Delta t_3|+|\Delta t_4|+|\Delta t_5|\over5}$

$\Delta t_{mean}={0+0.01+0.02+0.04+0.03\over5} = 0.02 s$

Percentage error $={\Delta t_{mean}\over t_{mean}}\times100$

$={0.02\over1.25}\times100=1.6\%$

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Nice explanation
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Thanks for your appreciation please share with your friends and tell them to create account for more nice explanation of there doubts and homework.
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0.02s is wrong the correct is 0.1
Maths  cal mistake
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@Jatin no its right can you elaborate more
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0.10/5=0.02
So it is correct only
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Clear explanation