A student measures times for 20 oscillations of a simple pendulum as 30s, 32s, 35s and 31s. If the minimum division in the measuring clock is 1s, then correct mean time in second , within error limits , is

Step-by-step solution

Mean time t_ mean = 30 + 32 + 35 + 31 4 = 128 4 = 32 s Absolute errors in each measurement are: t₁ = |30 - 32| = 2 s t₂ = |32 - 32| = 0 s t₃ = |35 - 32| = 3 s t₄ = |31 - 32| = 1 s Mean absolute error t_ mean = 2 + 0 + 3 + 1 4 = 6 4 = 1.5 s Since the minimum division (least count) of the measuring clock is 1 s , the mean absolute error must be rounded off to the nearest integer to match the precision of the instrument. Rounding 1.5 s to the nearest integer gives 2 s . Therefore, the correct mean time within error li