CHAPTER 11 MEASUREMENT AND DATA PROCESSING
(IB TOPIC 11) SUMMARY
Uncertainties and errors
Random uncertainties (or errors) arise mostly from inadequacy or limitation in the
instrument or the way a measurement is made. Random errors make a measurement less
precise, but not in any particular direction. These are written as an uncertainty range, such
as 44.20 Ä… 0.05 cm3.
Systematic errors are due to identifiable causes, and arise from flow in the instrument or
errors made in taking a measurement such as an incorrect calibration of a pH meter or
reading the top rather than the bottom of the meniscus. Systematic errors always affect a
result in a particular direction (always smaller or larger) unlike random errors. Random
uncertainties can be reduced by repeating readings; systematic errors can not reduced by
repeating readings.
Precision
If an experiment is repeated many times, the precision is a measure of how close the
repetitions will be to each other. The precision or reliability of an experiment is a measure
of the random error. If the precision is high then the random error is small.
Accuracy
The accuracy of a result is a measure of how close the result is to some accepted or
literature value Accuracy is a measure of the systematic error. If an experiment is accurate
then the systematic error is very small.
A measurement can have a great degree of precision, yet be inaccurate such as if the top
of a meniscus is read in volume readings using a pipette or a measuring cylinder instead
of he bottom of the meniscus.
Significant figures
The number of significant figures in any calculation should be based on the number of
decimal places/significant figures in the data based on the following simple treatment:
" In addition and subtraction: Add absolute uncertainties
" In multiplication, division and powers: Add percentage uncertainties
" If one uncertainty is much larger than the others, ignore the other uncertainties
and estimate the uncertainty based on the larger one using the rules above.
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