Two groups of six students are given different instruments to measure an object that has been exactly measured to have an accepted length of 0.47307 m. The measurements returned by the students in the groups are:
Group A: 18.625 in, 18.625, 18.750 in, 18.688 in, 18.563 in, 18.522 in
Group B: 47.50 cm, 47.50 cm, 47.38 cm, 47.47 cm, 47.48 cm
a) Convert each set of measurements to meters and find the mean length for each group. The conversion factors are 1 in = 2.54 cm and 1 cm =0.01 m. Remember that conversion factors are exact and do not affect the number of significant digits.
b) Given these mean values, which group took more accurate measurements? use the perfect error of the groups' mean values compared to the accepted length to justify your answer.
c) Which group had the more precise measurements? Use the mean deviation of the groups' data to justify your answer.
d) Given the measurements from each group, estimate the least count of the instrument they used. Remember that a measurement should include one estimated digit in addition to the least count.