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### 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

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/
```
Associated Topics:
Elementary Definitions
Elementary Measurement
Elementary Terms & Units of Measurement
Middle School Definitions
Middle School Measurement
Middle School Terms/Units of Measurement

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