Physics I Lab Manual 2011 15

# Physics I Lab Manual 2011 15 - ± 2 cm you could say that...

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EXPERIMENT 1. STATISTICS Figure 1.3: Graphical representation of how uncertainty in x aﬀects uncertainty in f ( x ) Frequently we wish to measure the same quantity in two diﬀerent ways to validate our mea- surements, or we wish to compare our measured values to the measurements that others have made. Because measurements have random errors we don’t expect multiple measure- ments of the same quantity to give the exact same results, however, we can use some basic statistical analysis to say how well they match. One common way to do that is to describe how far apart two values are in units of the total measurement uncertainty, for example if you measure the height of Alice to be h alice = 154 ± 2 cm (that is a measured value of 154 cm with an uncertainty of 2 cm) and you wish to ask if she is the same height as Bob who was measured to be 157
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Unformatted text preview: ± 2 cm you could say that their heights diﬀer by 3 cm with a total measurement uncertainty of 4 cm (There is 2 cm of uncertainty in Alice’s height and 2 cm uncertainty in Bob’s height), which allows us to say that the diﬀerence in their heights was measured to be 0 . 75 × the total measurement uncertainty. Generally if two values diﬀer by less than 1 × the total measurement uncertainty we say they “agree” with each other. In this case the measured height of Alice and Bob agree (i.e. they are the same height), given our measurement uncertainty – Alice could be anywhere from 152 cm to 156 cm, and Bob could be from 155 cm to 159 cm, so the measurement doesn’t exclude the possibility that they are the same height (for example they could both be 155.5 cm) 5...
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