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Are measured values and readings the same thing?

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Homework Statement


Are measured values and readings the same thing in error in measurement?

Homework Equations


Are measured values and readings the same thing in error in measurement?

The Attempt at a Solution


Error = True value - measured value
 

Answers and Replies

  • #2
hilbert2
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If someone says: "the reading of voltmeter was 0.274 V", is that complete enough to count as a serious measurement? What if they say: "A voltage of 0.27##\pm##0.2 V was measured"?
 
  • #3
kuruman
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Error = True value - measured value
This is meaningless.
Question: If you believe that the so called "true value" exists, how would you find out what it is?
Answer: You make a measurement.
Follow up: But the measurement always has an uncertainty built in it, so now what?
All you can provide with a measurement is a number and a bracket of uncertainty within which the value of the quantity that you are trying to determine most likely is. Think of it this way, the "true" value is by definition a number with zero uncertainty. How many significant figures might you need to express that number given the fact that it has zero uncertainty?
 
  • #4
jtbell
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Are measured values and readings the same thing in error in measurement?
To me, they are the same thing. Can you tell us why you suspect that they might not be the same thing? For example, something you've read, e.g. conflicting statements in two sources?
 
  • #5
hilbert2
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I would rather be inclined to say that a reading of a measuring device doesn't, in the strictest sense, tell you anything unless you know something about the probability distribution of the errors in the readings. Suppose I create a bogus digital voltmeter that produces completely random numbers between 1.00 and 100.00 volts. You can certainly obtain a "reading" from that device, but you don't really do anything useful with it.
 
  • #6
haruspex
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This is meaningless.
Question: If you believe that the so called "true value" exists, how would you find out what it is?
I don't see a problem here. Physics commonly assumes a true value exists, and it is quite reasonable to define the error in the measurement as measurement - true value (not the other way around). Stats theory does it all the time. It does not suppose you can ever determine the error value.
 
  • #7
haruspex
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If someone says: "the reading of voltmeter was 0.274 V", is that complete enough to count as a serious measurement?
Yes.
What if they say: "A voltage of 0.27±0.2 V was measured"?
I would say that the term "measurement" is widely used with both meanings. It can refer to an individual reading or to an estimate based on a set of readings.
I checked through several online academic resources and found they all use "measurement" in both senses in the same article. Generally they discriminate by calling a reading a single measurement.
 
  • #8
kuruman
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I don't see a problem here. Physics commonly assumes a true value exists, and it is quite reasonable to define the error in the measurement as measurement - true value (not the other way around). Stats theory does it all the time. It does not suppose you can ever determine the error value.
If the purpose of the measurement is to find a value that is closest to the true value of the observable, then the equation makes more sense to me as true value = measurement ± error, where "error" is estimated independently of "measurement". With "error" on the left side of the equation, it can be construed as being a means of finding the error in the measurement. All is fine so far, unless one measures a quantity that has an "accepted value", e.g. the acceleration of gravity. In that case the "true value" is often replaced with the "accepted value" of 9.8 m/s2 by people who don't know any better. Thus the "error" does not express the confidence in one's measurement given its conditions, but becomes the discrepancy between one's measurement and somebody else's measurement. The distinction between uncertainty in a measurement and discrepancy between measurements is often missed by beginners.
 

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