### Video Transcript

Which of the following statements
most correctly describes the meaning of the precision of measurements? A) A precise measurement is more
accurate than an accurate measurement. B) The more precise the measurement
of a quantity is, the closer the measured value is to the actual value of the
measured quantity. C) A precise measurement is made
using a correct measurement method. D) The more precise the measurement
of a quantity is, the smaller the predictable change that can be made between the
measured value and other measured values of the same quantity.

Okay, we can see that the answer to
this question is all about the specific meaning of the word precision when it comes
to making measurements. We have these four different
candidates for the most correct description of the precision of measurements. So let’s go through them one by one
and evaluate each in turn.

Option A says that a precise
measurement is more accurate than an accurate measurement. Now, one thing this option gets
right is that it acknowledges that there’s a difference between a precise
measurement and an accurate measurement. They don’t mean the same thing. But what it doesn’t get right is in
claiming that a precise measurement is more accurate than an accurate one. Because precision and accuracy are
two different terms with two different meanings, a precise measurement will not be
more accurate than an accurate one. We can cross off option A then.

Option B says that the more precise
the measurement of a quantity is, the closer the measured value is to the actual
value of the measured quantity. So option B is saying that we have
these two values: a measured one and the actual correct one for some quantity. And it says that the closer these
two values are, the more precise the measurement is. But this statement is confusing the
terms for precision and accuracy. If we replace this word “precise”
with the word “accurate,” then this description would be correct. The closeness of a measured value
to an actual true value is the meaning of an accurate measurement. But because precision and accuracy
don’t mean the same thing, Option B is not a correct description of a precise
measurement.

Moving on to option C, this says
that a precise measurement is made using a correct measurement method. Well, it’s certainly more likely
that using a correct measurement method will lead to a precise measurement. But that’s not always the case. It’s possible, for example, to have
a correct measurement method. But the way we carry out that
method has errors in it. And those errors, which would
influence the measurements we would make, might lead to imprecise measurements. Overall then, option C is not
looking like a great choice. But because it’s not explicitly
incorrect, let’s table it for now, keep it in mind, and then move on to our last
choice, option D.

This option says that the more
precise the measurement of a quantity is, the smaller the predictable change that
can be made between the measured value and other measured values of the same
quantity. Now here’s what this description is
saying. Let’s say that we have some true
value for a quantity. And we’ll call that value 𝑉. This could be the length of an
object or its mass. But the point is it’s the accurate
representation of that quantity. In order to discover what that
correct quantity is, we make a series of measurements. We can say that the result of our
first measurement is 𝑀 one. And then we make another
measurement 𝑀 two, another one 𝑀 three, and so on. We can make any number of these
measurements attempting to figure out the true value of the quantity we’re
interested in.

Now, statement D is not talking
about this true value 𝑉. What it’s comparing is the
different measured values of this quantity one to another. And it’s saying that the smaller
the difference between these measured values, the more precise our measurement
is. And this is a good description of
measurement precision. It compares measured values to one
another and says the closer they are to one another, the more precise our
measurements are. Since option D is an explicitly
correct description of the precision of measurements, we choose this as our
answer.