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- Question : 1E - Mean, standard deviation and standard error (1) An experiment was conducted to determine the concentration of a sodium hydroxide solution. The eight repeat measurements of the volume of hydrochloric acid titrated (all in ml) are: 25.8, 26.2, 26.0, 26.5, 25.8, 26.1, 25.8 and 26.3. Calculate (i) the mean, (ii) the standard deviation using the rough-and-ready approach; (iii) the standard deviation using eqn (2.3); (iv) the standard error of the volume.
- Question : 2E - Mean, standard deviation and standard error (2) 12 measurements of the sensitivity of a photodiode circuit (in amps/watt) are: 5.33, 4.95, 4.93, 5.08, 4.95, 4.96, 5.02, 4.99, 5.24, 5.25, 5.23 and 5.01. Calculate (i) the mean, (ii) the standard deviation using eqn (2.3); (iii) the standard error.
- Question : 3E - Reduction of the standard error In a magnetometry experiment, after a minute of collecting data the statistical noise was reduced to 1 picotesla. For how much longer should data be collected in order to reduce the random error by a factor of 10?
- Question : 4E - Error in the error Consider a set of measurements with the standard error calculated to be ? = 0.987 654 321. Here we address the question of how many significant figures should be quoted. Construct a spreadsheet with four columns. The first column should be N, the number of measurements on which ? is based. In the second column write ? to the nine significant figures quoted above. The third and fourth columns should be ?
- Question : 5E - Reporting results (1) Fifteen measurements of a resistance are quoted here, based on approximately 10 repeat measurements. Only three of them obey the five golden rules. Identify the mistakes in the other results. (i) (99.8
- Question : 6E - Reporting results (2) Analysis of a Rydberg spectrum yields a quantum defect, ?, for each line. How would you report the results if you obtain (i) ?
- Question : 7E - Significant figures Round up the following numbers to (a) two significant figures, and (b) four significant figures: (i) 602.20, (ii) 0.001 3806, (iii) 0.022 413 83, (iv) 1.602 19, (v) 91.095, (vi) 0.1660, (vii) 299 790 000, (viii) 66.2617, (ix) 0.000 006 672 and (x) 3.141 593.
- Question : 8E - Scientific notation Rewrite the ten numbers from Exercise (2.7) in scientific notation.
- Question : 9E - Superfluous precision A car covers a distance of 250 m in 13 s; the average speed is calculated to the 10 decimal places of the calculator as 19.230 769 23 m s?1. Explain why it is incorrect to believe all of the significant figures of the quoted speed.

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