Accuracy vs. Precision
- Accuracy is how close
a measurement or estimate is to the correct value.
- Precision is how exact and reproducible a measurement or estimate
is.
- Notice that I stressed the fact that we are talking about measured or estimated
data. Pure numbers like exact counts or numerically defined numbers have infinite
precision and accuracy
- If I count the number of people in this room to be 24 then
that is perfectly accurate (assuming I counted correctly) and infinitely
precise.
- The equivalence 1 in = 2.54 cm is determined by definition. These numbers,
when used in doing conversions would be considered to be both perfectly
accurate and precise.
- Below is a joke I found at http://www.mpce.mq.edu.au/~malcolmt/measrmnt/sigfigs.htm
A group of Civil Engineers were at a conference being
held in Central Australia. As part of the conference entertainment, they were
taken on a tour of the famous rock, Uluru.
"This rock", announced the guide, "is 50,000,004 years old."
The engineers - always impressed by precision in measurement - were astounded.
"How do you know the age of the rock so precisely?" asked one of the group.
"Easy!", came the reply. "When I first came here, they told me it was 50 million
years old. I've been working here for four years now."
-
- Below is a data table produced by three groups of students who were measuring
the mass of a paper clip which had a known mass of 1.0004g.
| |
Group 1 |
Group 2 |
Group 3 |
Group 4 |
| |
1.01 g |
2.863287 g |
10.13251 g |
2.05 g |
| |
1.03 g |
2.754158 g |
10.13258 g |
0.23 g |
| |
0.99 g |
2.186357 g |
10.13255 g |
0.75 g |
| Average |
1.01 g |
2.601267 g |
10.13255 g |
1.01 g |
-
- Notice that Group 1 had data that was precise (in terms of
consistency) and the average was very close to the correct answer (accurate).
- Group 2 had data that looks precise (many numerical digits of information).
However, it is not very accurate. Notice that whatever instrument they
are using to measure with really only gives measurements that are consistent
to the tenths place. It makes no sense for them to record all the other
digits. This answer should really be only reported to one decimal place
(2.6 g).
- Group 3 had data that was very precise (both consistent and lots of
digits) however it is not very accurate. What might cause this type of
error in their data?
- Group 4 looks like Group 1, but their answers are very different. Group
4's answer just happened to come out to the same as Group 2. Their data
is all over the place (very imprecise).