The period of oscillation of a simple pendulum is measured, in successive measurement the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s.
Then, the relative error or percentage error is
The mean period of oscillation of the pendulum is
As the periods are measured to a resolution of 0.01 s, all times are to the second decimal, it is proper to put this mean period also to the second decimal. The errors in the measurement are
2.63 s –2.62 s = 0.01s
2.56 s –2.62 s = –0.06 s
2.42 s –2.62 s = –0.20 s
2.71s –2.62 s = 0.09 s
2.80 s –2.62 s = 0.18 s
Note that the errors have the same units as the quantity to be measured. The arithmetic mean of all the absolute errors (for arithmetic mean, we take only the magnitudes) is
= 0.54 s / 5 = 0.11s
That means, the period of oscillation of the simple pendulum is or between 2.73 s and 2.51 s. As the arithmetic mean of all the absolute errors in 0.11 s, there is already an error in the tenth of a second. Hence, there is no point in giving the period to a hundredth. A more correct way will to be write,
Note that the last numeral 6 is unreliable, since it may be anything between 5 and 7. We indicate this by saying that the measurement has two significant figures. In this case, the two significant figures are 2, which is reliable and 6, which has an error associated with it. Hence, the relative error or percentage error is