14. A laboratory mass balance is used to determine the mass of a textbook, and shows the mass to be 2.543798 Kg. A fishing scale is used to measure the mass of the same book, and shows the mass to be 2.54 kg. Which of the following statements is the most correct?
a) The fishing scale is less accurate.
(b) The fishing scale is less precise
c) The fishing scale is more accurate
(d) Neither scale is accurate

 

Is there any choices you can clearly say are NOT the answer?

 

What does it mean for a scale to be "accurate"?

What does it mean for a scale to be "precise"?

What if the actual, true mass of the textbook is 2.541 kg?

What if the actual, true mass of the textbook is 2.59363145 kg?

 

Accuracy is a measure of how close the measurement is to the actual value (as determined by some absolute standard).
Precision is how repeatable a measurement is to a given number of decimal points (usually to ± one LSB). Thus the more precision, the more digits can be used for the measured value.

Thus a measurement can have high precision but poor accuracy (which can be okay if all you want is the difference between two measurements).
For example, a digital voltmeter could have 6-digit precision and linearity, but if the calibration is off, would have poor accuracy.

Base upon those definitions, sama3505, what answer would you say is most correct?

 

Thanks @crutschow
you have defined it perfectly more than i expected ,So according to your definitions I prefer answer
a) The fishing scale is less accurate ,
because fishing scale has a round value ,and lab mass balance has a exact accurate value .

 

Thanks @crutschow
you have defined it perfectly more than i expected ,So according to your definitions I prefer answer
a) The fishing scale is less accurate ,
because fishing scale has a round value ,and lab mass balance has a exact accurate value .

Sorry, no, you got it backwards.
Reread my definitions.
We know nothing about the accuracy of either scale, as they both could be reading the same incorrect value.
All we know is that the lab mass balance indicates a higher precision reading than the fishing scale so the answer should be
(b) The fishing scale is less precise.

 

Yeh great ,now i got it ,, we can not say anything about accuracy ,true

Thanks @crutschow

 

But we also have no idea about the precision of either scale. Just because something displays more digits does NOT mean that it is either more accurate or more precise.

Think about it -- the definition you have: Precision is how repeatable a measurement is. How can anyone say anything about the precision of a device based on one measurement?

Just as without knowing the actual mass of the object we can't say anything about the accuracy of either instrument, without repeated measurements we can't say anything about the precision of either device. While it is true that we EXPECT a lab balance to be both more accurate and more precise than a fishing scale, we have no basis upon which to claim that THIS lab balance is either more accurate or more precise than THIS fishing scale.

 

But we also have no idea about the precision of either scale. Just because something displays more digits does NOT mean that it is either more accurate or more precise.

Think about it -- the definition you have: Precision is how repeatable a measurement is. How can anyone say anything about the precision of a device based on one measurement?

Just as without knowing the actual mass of the object we can't say anything about the accuracy of either instrument, without repeated measurements we can't say anything about the precision of either device. While it is true that we EXPECT a lab balance to be both more accurate and more precise than a fishing scale, we have no basis upon which to claim that THIS lab balance is either more accurate or more precise than THIS fishing scale.

Yes, you would have to make the assumption that the "laboratory mass balance" is well enough designed that the digits shown represent its precision.
I think that's a reasonable assumption, but you may disagree.
Without that assumption, none of the answers are correct.

 

Yes, you would have to make the assumption that the "laboratory mass balance" is well enough designed that the digits shown represent its precision.
I think that's a reasonable assumption, but you may disagree.
Without that assumption, none of the answers are correct.

But if we are willing to assume that a "laboratory mass balance" is well enough designed that the digits shown represent its precision, why isn't it just as reasonable to assume that a "laboratory mass balance" is well enough designed that the digits shown also represent its accuracy (at least in comparison to a fishing scale)?

Let's consider for a moment what we are basing the answer to the question on. Is it really on the data presented? What if the question has said that it was "Bob's homebrew mass balance" instead of being a laboratory mass balance, but everything else was left the same. Would you still claim that it was reasonable to assume that Bob's homebrew mass balance was more precise merely because more digits were given? Probably not. So the claim that it is more precise isn't based on the data, it is really on based on the statement that it is a laboratory mass balance -- a laboratory mass balance that may or may not have been abused and damaged or just gotten a lot of gunk in the pivots or what have you since it was built -- so the question might as well leave out the readings altogether and merely say that a laboratory mass balance indicated X kg and a fishing scaled indicated Y kg.

 

"Which of the following statements is the most correct?"

The keyword is most. That takes the nit-picking out of it. That means you guess with info given.

It means your selection doesn't have to meet every definition and qualification.

Because the question didn't.

 

Considering that (a) and (c) are mutually exclusive and that the chance of them being equally accurate is negligible, then wouldn't the answer have to be either (a) or (c)? I mean, if you say that (a) is not correct, then (c) must be correct, no?

It's a poorly crafted question, probably crafted by someone that doesn't understand these concepts themselves.

And, yes, that same person almost certainly intended the "correct" answer to be (b).

 

Poorly crafted question? Maybe it was crafted to intentionally confound.

It works.

 

Poorly crafted question? Maybe it was crafted to intentionally confound.

It works.

I doubt that. Most likely the person that wrote it was making certain assumptions without realizing that the question didn't convey the necessary information to make those assumptions valid on the part of the reader. That's always a risk when writing questions. I always have several every semester where I've written a question where I've thought everything was well-defined only to have someone interpret it wrongly. Now, in many cases I can't see that their interpretation is warranted and usually I can point out where their interpretation is flawed. But sometimes I have to admit that their interpretation, even if it might clearly be reflective of weak understanding of the concepts, is never-the-less as more-or-less valid interpretation from their perspective.

 

Considering that (a) and (c) are mutually exclusive and that the chance of them being equally accurate is negligible, then wouldn't the answer have to be either (a) or (c)? I mean, if you say that (a) is not correct, then (c) must be correct, no?
............

Yes.
But just because two answers are mutually exclusive doesn't mean that we can determine which is the correct answer from the given information.

 

Yes.
But just because two answers are mutually exclusive doesn't mean that we can determine which is the correct answer from the given information.

I agree. But since one of them must be correct, would that not exclude all of the OTHER answers from consideration?

The answer to this question is not clear cut as there are reasonable arguments for both possible answers.

Of course, this is assuming that it is a single-answer multiple choice question (my wife ran into a cultural issue when she took her first "multiple choice" exam in grad school here because, in Taiwan, the term "multiple choice" is used for exams where there might be multiple correct answers and you have to mark all of them).

 

Sorry, no, you got it backwards.
Reread my definitions.
We know nothing about the accuracy of either scale, as they both could be reading the same incorrect value.
All we know is that the lab mass balance indicates a higher precision reading than the fishing scale so the answer should be
(b) The fishing scale is less precise.

so they asking for the most correct .
even we can say Neither scale is accurate .(OR WE CANT, because we have not much values to compare)

 

so they asking for the most correct .
even we can say Neither scale is accurate .(OR WE CANT, because we have not much values to compare)

That is most likely the answer they are looking for. But I contend that one of two things is true. Either they didn't think through the question very well, or they are actively teaching students something that isn't true, namely that you can tell something about either the accuracy or the precision of a measurement based on how many digits are written down. While that might often be the case in practical situations (but it is still often NOT the case, even in practical situations), the material being taught is clearly about the theory of measurement concepts. The accuracy and precision of a measurement is dictated by the instrumentation and the method by which the measurement is made. How the result is displayed can place an upper bound on either, but it cannot improve either one.