Video Transcript
Which of the following statements
does not correctly describe the relationship between the precision of a set of
measurements and the resolution of a measuring instrument that makes the
measurements? (A) The precision of measurements
is affected by uncontrolled experimental variables changing the values of the
quantities being measured. The resolution of a measuring
instrument is not affected by changes in the values of measured quantities. (B) The precision of measurements
cannot be better than the resolution of the instrument that makes them. (C) The resolution of a measuring
instrument can be applied to single measurements of a value, but precision can only
be applied to a set of measurements. (D) The resolution of a measuring
instrument cannot be better than the precision of the measurements made by that
instrument.
To answer this question, we need to
understand the relation between the precision of a set of measurements and the
resolution of the instrument used to make the measurements. Let’s start by thinking about these
two terms: precision and resolution.
The precision of a set of
measurements is a measure of how close together the measurements are. For example, say that we used a
ruler to measure the length of a pencil. Let’s say that the first time we
measure its length, we take two readings, and the results are 99 millimeters and 101
millimeters. Now, let’s say that we repeat the
measurements and take a second set of readings. For whatever reason, this time we
measure 90 millimeters and 110 millimeters. In set one, the readings are two
millimeters apart from each other. In set two, the readings are 20
millimeters apart. So, in set one, the readings are
closer together than in set two. And therefore, set one is the more
precise set.
Now, let’s think about the term
resolution. The resolution of an instrument is
the smallest unit that the instrument can legitimately measure. Let’s go back to our example of a
ruler. A ruler is usually marked with a
scale that goes up in millimeters so that the distance from one line to the next is
one millimeter. So imagine that we measure our
pencil, but the end of the pencil doesn’t line up exactly with the lines on the
ruler. Instead, the end of the pencil is
somewhere between the 100-millimeter mark and the 101-millimeter mark on the
ruler.
Looking at this, it isn’t possible
to say exactly how long the pencil is, because it isn’t perfectly lined up with a
mark on the ruler. All we can really say is that the
pencil length is closer to 101 millimeters than it is to 100 millimeters. Because the lines of the ruler are
one millimeter apart, we’re only able to measure the length of the pencil to the
nearest one-millimeter increment. This is the resolution of the
ruler, one millimeter.
So, we’ve seen that the precision
of a set of measurements depends on how close together the values of the
measurements are. Also, we’ve seen that the
resolution of a measuring instrument is the smallest unit that the instrument can
reliably measure. With this in mind, let’s look at
our options for this question and decide which one of these statements is not
true.
We’ll clear some space to make room
for a shortened version of option (A). This option essentially says
“Measurement precision is affected by uncontrolled variables that change the values
of measured quantities. Instrument resolution is not
affected by those changes.” Let’s think about the first
sentence. Can the precision of measurements
be affected by uncontrolled experimental variables? Well, yes. A variable is just something that
changes while the experiment takes place. We typically try to stop this by
attempting to control a variable, but if we can’t control all variables, then our
measurements will be affected. Usually this does happen to a
certain degree, so we have measurements that aren’t totally precise.
For example, let’s say we wanted to
measure the length of our pencil three times. An important variable is which
pencil we measure. If we measure the same pencil three
times, we would expect our results to be close together and therefore pretty
precise. But, let’s say we forgot to control
this variable, and we measured the lengths of three completely different
pencils. The values we measured would be
very different from each other and therefore much less precise.
So, uncontrolled experimental
variables can affect the precision of our measurements. But can they affect the resolution
of our instrument? Well, no. Concerning resolution, it doesn’t
matter which pencil we measure because the markings on the ruler won’t be affected
by what’s being measured. The ruler is still the same, so the
resolution doesn’t change. This means that option (A)
correctly describes precision and resolution. To answer this question, we’re
looking for a statement that isn’t correct. So, (A) can’t be the answer.
Let’s move on to option (B): the
precision of measurements cannot be better than the resolution of the instrument
that makes them. Again, imagine we’re measuring the
length of our pencil using a ruler. When this is the case, the smallest
possible difference between two values is one millimeter. For example, we could measure the
length of the pencil twice and get two values: 100 millimeters and 101
millimeters. To find the precision of these
measurements, we simply find the difference between them, one millimeter. One millimeter is also equal to the
resolution of the ruler.
We cannot accurately measure two
different values more precisely than this, because the accuracy of the measurements
is limited by the resolution of the ruler. The precision of measurements
cannot be better than the resolution of the instrument we use to measure. So, statement (B) is true; it isn’t
the answer we’re looking for.
Next, let’s think about (C): the
resolution of a measuring instrument can be applied to single measurements of a
value, but precision can only be applied to a set of measurements. It’s true that the resolution of a
measuring instrument can be applied to a single measurement. In fact, every time we make a
measurement, we have to bear in mind the resolution of our instrument. It is also true that precision can
only be applied to a set of measurements.
Remember that precision tells us
how close together the values in a set of measurements are. If we only have a single value, it
doesn’t make any sense to say it’s close to itself. So, precision can only be applied
to a set of two or more measurements. So, option (C) is also true, and we
should eliminate it.
Finally, let’s look at (D): the
resolution of a measuring instrument cannot be better than the precision of the
measurements made by that instrument. Actually, it’s perfectly possible
and very common for the resolution of the measuring instruments to be better than
the precision of the measurements made. For example, we could measure the
length of the pencil twice and get the values of 99 millimeters and 101
millimeters. To find the precision of these
measurements, we find the difference between them, two millimeters.
But the resolution of the ruler is
still one millimeter, because the markings on the ruler are still one millimeter
apart. So, the resolution of a measuring
instrument can be better than the precision of the measurements made by the
instrument. So, option (D) is not a correct
statement. This means that the answer to this
question is option (D).
