Time interval measured by a clock given the following reading 1.25s, 1.24s 1.27s 1.21s, 1.28s what is% relative error

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Solution

Step 1,
The time interval measured by the clock is given
True value will be the mean of the readings
So,
True value = Mean = $a = \frac{1.25 + 1.24 + 1.27 + 1.21 + 1.28}{5} = 1.25$
Now, error in each reading will be given as
$Δ a_{1} = 1.25 - 1.25 = 0$
$Δ a_{2} = 1.25 - 1.24 = 0.01$
$Δ a_{3} = 1.25 - 1.27 = - 0.02$
$Δ a_{4} = 1.25 - 1.21 = 0.04$
$Δ a_{5} = 1.25 - 1.28 = 0.03$
Step 2,
Now we will find the mean of errors
Mean = $Δ a = \frac{0 + 0.01 + 0.02 + 0.04 + 0.03}{5} = 0.05$
Now relative error = $\frac{Δ a_{m e a n}}{a_{m e a n}} \times 100 = \frac{0.05}{1.25} \times 100 = 4 %$
Hence the relative error is 4%

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