In Sections 5 and 6 we saw two different specifications for the error in a directly measured quantity: the standard deviation and the reading error. Both are indicators of a spread in the values of repeated measurements. They both are describing the precision of the measurement.
The word precision is another example of an everyday word with a specific scientific definition. As we shall discuss later, in science precision does not mean the same thing as accuracy.
In any case, we now have two different numbers specifying the error in a directly measured quantity. But what is the error in the quantity?
The answer is both. But fortunately it is almost always the case that one of the two is much larger than the other, and in this case we choose the larger to be the error.
In Exercise 6.1 you measured the thickness of a hardcover book. Unless the book has been physically abused the standard deviation of your measurements was probably negligible and might even have been zero. Thus the error in your measurement is just the reading error.
In other cases, such as the number of radioactive decays in one second that we looked at in Sections 4 and 5, the reading error of the digital Geiger counter is ± 0.5 counts, which is negligible compared to the standard deviation. Thus here the error in each measurement is the standard deviation.
Often just thinking for a moment in advance about a measurement will tell you whether repeating it will be likely to show a spread of values not accounted for by the reading error. This in turn will tell you whether you need to bother repeating it at all.
If you don't know in advance whether or not you need to repeat a measurement you can usually find out by repeating it three or four times. If repeated measurements are called for, we will discuss in Section 10 how many repetitions is ideal.
This document is Copyright © 2001, 2004 David M. Harrison
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