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CHEM 2121
Nicholas Frost

When youre givenvalues use the error propagation rules first digit of uncertaintylast digit of actual answer otherwise just use normal sig fig rulesif need to propagate error and something doesnt give it to you just assume 1 in the digit of uncertaintysee table 31 on p 61 of textbook to see other rules for error propagation for other operationsstandard deviation show near data points are to each otherprecisionocant improve standard deviation by taking more measurements bc random error is always presentostandard deviations about the glassware you use other sources of error notmeasurements2osvarianceoCoefficient of variation relative standard deviation100sxbarstandard deviation expressed as percentage of mean valuefrom data set can calculate mean slope and interceptCan improve confidence interval more measurements can see in formula since n is in denominatoroalso as n increases t decreases so reinforce that effectonote need a LOT of samples to measure to have any significant improvement in confidenceHow to tell if means are actually significantly differento1 Calculate meano2 Calculate standard deviationso3 Do F testo4If FcalcFtable use spooled and tcalc w spooled DOFn1n22If FcalcFtable use tcalc which has separate s1 and s2 and then use DOF eqn round down vs rounding upo5 Depending on which t value you calculated compare it to tableif tcalcttable not significant difference but not sure that its actually the same eitherif tcalcttable 95 confident that the differencesignificant 95 sure that the 2 populations we are comparing have different true means mu valuessystematic error is present but dont know which population has it or if even both have itStandard Deviation of the Mean of sets of n valuesSqrtnnoHere instead of measuring each thing at a time you can measure nat the same time repeat process of measuring n things at a time many times from this can calculate meanand standard deviation no is smaller than justpopulation standard deviationnothe more times you measure quantity the more confident you are that avgclose to population meanouncertainty decreases by Sqrtn timesoreview this againMethod of Least Squares subconsciously use this when we sketch line of best fit
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