17.1 A group of students uses a pendulum experiment to measure g, the acceleration of free fall, and obtains the following values (in m s-2): 9.80, 9.84, 9.72, 9.74, 9.87, 9.77, 9.28, 9.86, 9.81, 9.79, 9.82. What would you give as the best value and standard error for g as measured by the group?

We first note that the reading of 9.28 m s-2 is so far from the others that it is almost certainly in error and should not be used in the calculation. The mean of the ten remaining values is 9.802 and the standard deviation of the sample about its mean is 0.04643. After including Bessel's correction factor, the estimate of the population s.d. is σ = 0.0489, leading to a s.d. in the measured value of the mean of 0.0489/√10 = 0.0155. We therefore give the best value and standard error for g as 9.80 ± 0.02 m s-2.

17.3 The following are the values obtained by a class of 14 students when measuring a physical quantity x: 53.8, 53.1, 56.9, 54.7, 58.2, 54.1, 56.4, 54.8, 57.3, 51.0, 55.1, 55.0, 54.2, 56.6.

1. (a) Display these results as a histogram and state what you would give as the best value for x.

2. (b) Without calculation, estimate how much reliance could be placed upon your answer to (a).

3. (c) Data books give the value of x as 53.6 with negligible error. Are the data obtained by the students in conflict with this?