Which of the following is the correct definition of the accepted or actual value of a quantity? (A) The average measured value of the quantity. (B) The value of the quantity that occurs most frequently when the value is measured. (C) The value of the quantity the first time it was ever measured. (D) The value of the quantity when it is not altered by any measurement errors. (E) The most recently measured value of the quantity.
This question is asking us to recall what is meant by the accepted or actual value of a quantity. We can recall that when we measure the value of a quantity in an experiment, we usually compare that value to the accepted or actual value for that quantity. Moreover, we often assess the accuracy of a measurement by how closely the measured value matches the accepted value. We expect that a perfect experiment with no factors affecting the measurement will always give the true exact value for a quantity. And the more accurate a nonideal experiment is, the more closely we expect its results to match an ideal experiment.
So, since we assess the accuracy of a measurement by comparing the value to the accepted value and the more accurate a measurement is, the more we expect its results to match an ideal measurement, we can see that the accepted value of a quantity must be something similar to the true value of the quantity when it is not affected by any other factors. Of the available choices, the definition that most closely describes a value that is not affected by other outside factors is choice (D), the value of the quantity when it is not altered by any measurement errors. And indeed this is the definition of the accepted value of a quantity.
It’s worth understanding why using any of the other four choices as a definition for the accepted value would not give us a good standard by which to judge other experiments. This is most easy to see for choices (C) and (E). Choice (C) suggests that the definition should be the value of the quantity the first time it was ever measured. However, we know that scientific equipment constantly improves in its accuracy. So, assuming we’re using the best equipment available, we actually expect that the first time the value of a quantity is measured will be the least accurate measurement. Because subsequent measurements will be taken with equipment that is more accurate and less prone to error. So choice (C) doesn’t make much sense for a definition of the accepted value of a quantity.
Now, if measurement equipment is constantly improving, we might be tempted to choose choice (E), the most recently measured value for the quantity. But this too would not provide us with a robust standard for comparison. All scientific measurements have some amount of error and uncertainty. And we cannot be sure of those results until they’re independently repeated. So just because a value is recently measured does not make it accurate.
If we cannot assume that the first measurement of a quantity is correct, nor can we assume that the most recent measurement of a quantity is correct, perhaps we should assume that the most common value for the measurement is correct. But this too would not provide us with a value that is guaranteed to be accurate. This is because different types of measurement have different inherent measurement errors regardless of how many times the measurement is performed. In other words, measuring the same inaccurate value 100 times does not make that inaccurate value any more accurate.
Finally, choice (A), the average measured value of the quantity, suffers from the same problem as choice (B). The average measured value of a quantity will be affected by the measurement errors of each value that went into calculating that average. Of our choices, only (D) is not affected by the measurement errors of any particular measurement and is, therefore, the best option for the standard by which we judge other measurements.