A student conducted an experiment
and obtained three values during three repetitive trials: 1.55, 1.75, and 2.25. Later, the student discovered that
the true value was 1.85. In contrast to the real value, the
experimental results should be characterized as blank. (A) Not accurate and not precise,
(B) accurate but not precise, (C) not accurate but precise, (D) accurate and
precise, or (E) accurate and precise but unreliable.
This question is asking us to
comment on accuracy and precision in relation to an experiment. Accuracy and precision are
technical terms with a very specific meaning when it comes to discussing scientific
Accuracy is a measure of how close
your experimental result is to the true value. You can think of this as the
difference between your experimental result and the true value. On the other hand, precision is a
measure of the variation between the repeated results. So you can think of this as a
measure of how close each of your values is to the other values that you
So accuracy is how close you are to
the real value, and precision is how close each of your values is to each other. So let’s try to visualize what this
might look like. We can think of these in terms of
targets. These could be archery targets or
dart boards, for example. If we were to throw four darts at
one of our dart boards and they landed like this, we would describe this as both
accurate and precise, accurate because all four of your darts have landed near the
bull’s eye and precise because all of your darts are closely grouped together.
If you threw another set of darts
and they landed like our second target, we would describe this as not accurate but
still precise. These are not accurate because they
haven’t landed near the bull’s eye. But they’re still precise because
all four darts are closely grouped together.
If you threw another set of darts
and they landed like our third target, we would describe this as accurate but not
precise. They are accurate because if you
were to average them out, you would reach somewhere very close to the bull’s
eye. However, it’s not precise because
our darts are not closely grouped together. Instead, they are spaced out. So this makes them not precise.
If you threw a final set like this,
we would describe this as not accurate and not precise. They are not accurate because
they’re not anywhere near the bull’s eye. And they are not precise because
they are not closely grouped together.
Now, let’s try to visualize these
concepts in terms of the experiment in our question. In our question, we are told that
the true value of whatever it is that we’re measuring is 1.85, which would be about
here on our scale. The values that our student
measured were 1.55, 1.75, and 2.25. Now, we have to decide whether
these results are accurate or precise.
Let’s start by looking at
accuracy. All three of our student’s
measurements surround the true value. And let’s see what happens if we
average them out. If we add all three measurements
and divide by three, we actually get 1.85, which is the same as the true value. Since accuracy is a measure of how
close your results are to the true value, we can say that, in this experiment, our
results are accurate. This means we can rule out any
answers which say “not accurate.”
Next, we need to look at
precision. Remember that precision is a
measure of how close each of our results is to one another. By looking at our line, we can see
that our three values are actually quite spread out rather than being closely
clumped together. This makes our results not
precise. This means we can rule out answers
(D) and (E).
So the results from the experiment
in the question should be characterized as accurate but not precise. It’s worth mentioning that answer
(E) mentions the term “unreliable.” Reliability is a measure of how
close one experiment’s results are to another experiment and another, et cetera. As we only have one experiment
given in the question, we’re not able to comment on reliability from the information
given. So this is another reason why (E)
is an incorrect answer.