Measurement: Precision vs. Accuracy
Date: 01/07/2003 at 01:08:38 From: Shirlee Subject: Metric units Using a metric ruler student A measured the length of an object to the nearest tenth (0.1) of a centimeter, while student D measured its length to the nearest centimeter. Which measurement is more accurate?
Date: 01/07/2003 at 12:27:45 From: Doctor Peterson Subject: Re: Metric units Hi, Shirlee. I believe the question is asking which of them gives a length that is closer to the actual length. We can't quite answer that question without making some assumptions; but discussing why will help you understand more about the concept. We have to distinguish between "accuracy," which means the closeness of a measurement to the exact value, and "precision," which means the claimed or implied closeness. For example, if I said my desk was 2 meters wide, and you said it was 2.345 meters wide, your answer would be more precise (claiming that you know it down to the millimeter); but if the desk is really 2.123 meters wide, then my answer is more accurate! Now, we are told that each student measured the object with a different precision, one showing tenths and the other showing only centimeters. That says nothing about who is more accurate, since either of them might have made a mistake. But let's assume they both did their work correctly. How far can each of them be from the exact length? Suppose A said it was 3.1 cm long. Then, if he is right, it can be anywhere from 3.05 to 3.15 cm in reality; anything less than 3.05 would have rounded down to 3.0 (the nearest tenth), and anything more than 3.15 would have rounded up. So he can be off by no more than 0.05 cm. Similarly, if D said it was 3 cm long, it might really be anywhere from 2.5 to 3.5 cm, and his maximum error is 0.5 cm. So A is likely to be more accurate, because he is TRYING to be more accurate by being more precise AND by measuring carefully. But he may NOT be more accurate. Suppose that the actual length is 3.05 cm. Then 3 cm and 3.1 cm are equally far from the correct length. The same will happen if the correct length is 3.02, so that A gives 3.0 and D gives 3 cm. So A will never be LESS accurate, but they might happen to be equally accurate. Does that help? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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