Lecture # 4 Feb. 5th 2007. Errors

Three types of error: random (just as likely to be positive or negative), systematic (causes unidirectional bias) and blunder (may be unnoticed).

Random errors are dealt with by the application of statistics. Systematic errors can be corrected, but blunders may only be noticed if you know what the result should be. Watch out for digit transposition, missing factors of ten, and stoichiometric coefficients in the denominator when they should have been in the numerator (or vice versa)

The results of calculations are rounded off to the appropriate numbers of significant figures (all the digits known with certainty plus the first uncertain digit).

For additions and subtractions the number with least number of decimal places governs the number of decimal places in the answer, and hence the number of significant figures.

For multiplication and division, the number with the least number of significant figures governs the number of significant figures in the answer.

If the plus or minus (±) terms are known, then the overall ± term may be calculated.

For addition and subtraction the overall uncertainty (±) is the square root of the sum of the squares of the individual ± terms (note slight error in my lecture).

For mult. and divn. the overall relative uncertainty [that is the ± term divided by the answer] is the square root of the sum of the squares of the individual relative uncertainties.

It is important that the result of any analysis be accompanied by information about the uncertainty. The ± term is a good way to do this. You will need to explain what the ± term is, as it could be a standard deviation or, more commonly, a 95% confidence interval.