Accurate, precise, both, or neither?

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Homework Help Overview

The discussion revolves around the concepts of accuracy and precision in the context of measuring the density of water. The original poster presents measured values from three trials and questions whether these measurements can be considered accurate, precise, both, or neither.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definitions of accuracy and precision, questioning the closeness of the measurements to each other and to the actual value. There is discussion about the mean of the measurements and how it relates to the actual value. Some participants suggest that the determination of accuracy may depend on the required precision level.

Discussion Status

The discussion is ongoing, with participants raising questions about the definitions and implications of accuracy and precision. There is no explicit consensus, but various interpretations and considerations are being explored, particularly regarding the mean of the measurements and the standards for accuracy.

Contextual Notes

Participants note that the assessment may depend on the required precision level, indicating that the context of the problem may impose constraints on the definitions being discussed.

Lori

Homework Statement


1.9584 is the measured density of water...

student measures 3 trials:
1. 1.9141
2. 1.9584
3.1.8991

Homework Equations


Precise - the closeness of the measurements to each other
accuracy- the closenses of measures to the actual value

The Attempt at a Solution


I'm thinking it's neither precise or accurate. The values are not close to 1.9583, they differ quite different given that the actual measured values have more decimal places.

Also, it wouldn't be precise because they all different greater than 0.01
 
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Lori said:
Also, it wouldn't be precise because they all different greater than 0.01
Depends on your standards, but a 0.5% precision shouldn't be too hard, yes.
Lori said:
The values are not close to 1.9583, they differ quite different given that the actual measured values have more decimal places.
What is their mean? How much does that differ from the precise value, if you consider the spread of the measurements?
 
mfb said:
Depends on your standards, but a 0.5% precision shouldn't be too hard, yes.What is their mean? How much does that differ from the precise value, if you consider the spread of the measurements?
the mean is 1.9239 which is like 0.03 away from the actual measurement. Would this make it accurate?
 
It is not sufficient to tell if many measurements would have the right average or not.
 
Lori said:
the mean is 1.9239 which is like 0.03 away from the actual measurement. Would this make it accurate?
Define "accurate" !

If the specification is that you need accuracy to two decimal places, then yes. If you need it to 8 decimal places, then no.
 
Just as an aside, and not because I think you don't understand the difference between precision and accuracy, this is how I was taught to remember the difference.

How do you get from Washington DC to the middle of Texas?
Precise answer: <long set of very detailed directions that ends you up somewhere near Boston.>
Accurate answer: Go to Oklahoma and turn left.​
 
mfb said:
It is not sufficient to tell if many measurements would have the right average or not.
I wasnt sure of the answer because it was multiple choice. So, i just picked neither precise or accurate
 

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