Question

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

Answer 1

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

$\Delta a_1=1.25-1.25=0$

$\Delta a_2=1.25-1.24=0.01$

$\Delta a_3=1.25-1.27=-0.02$

$\Delta a_4=1.25-1.21=0.04$

$\Delta a_5=1.25-1.28=0.03$

Step 2,

Now we will find the mean of errors

Mean = $\Delta a=\frac{0+0.01+0.02+0.04+0.03}{5}=0.05$

Now relative error = $\frac{\Delta a_{mean}}{a_{mean}}\times 100=\frac{0.05}{1.25}\times 100=4\%$

Hence the relative error is 4%