Question

​A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

Answer 1

Let’s first find the mean value of time:
=
1 +2 +3 +4 4
=
90 +91 +95 +92 4
=
368 4
= 92 .
Then, we can find the absolute error for each measurement: ∆1 = | −1| = |92 −90 | = 2 , ∆2 = | −2| = |92 −91 | = 1 , ∆3 = | −3| = |92 −95 | = 3 , ∆4 = | −4| = |92 −92 | = 0 .
Let’s calculate the mean absolute error:
∆ =
∆1 +∆2 +∆3 +∆4 4
=
2 +1 +3 +0 4
=
6 4
= 1.5 ≈ 2 .
Therefore, the reported mean time should be 92±2 .