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4. Uncertainty calculations
Volume measurement, weighing, reaction temperature, reagent purity, and the value assigned to the calibrator are all examples of sources of uncertainty in our profession.
4.1. Uncertainty in a single measurement
Tyler weighs himself on his bathroom scale. The smallest divisions on the scale are 1-pound marks, so the least count of the instrument is 1 pound. Tyler estimates his weight to be at 142 pounds. He knows that his weight must be greater than 141.5 pounds (otherwise it would be closer to 141 pounds), but less than 142.5 pounds (or else it would be closer to the 143-pound mark). So Tyler’s weight must be:
weight = 142 +/- 0.5 pounds (4.1)
In general, the uncertainty in a single measurement from a single instrument is half the least count of the instrument.
4.2. Calculation of uncertainty of a slope on a graph.
If there are more than a few points on a graph, the uncertainty in the slope should be calculated as follows. The data points are represented by small, filled black circles in the diagram below; each datum contains error bars to reflect the degree of uncertainty in each measurement. It appears that current and voltage are measured to be within +/- 2.5 milliamps and +/- 0.1 volts, respectively. Points used to calculate slopes are represented by hollow triangles.
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