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/