### Video Transcript

10 students are measuring mass with
a malfunctioning balance. The malfunctioning balance always
displays values that are 40 percent too large. The students determine a total of
20 mass values for a single heap of caustic soda. All of their mass measurements are
between 100.1 and 100.3 grams. What combination of words should be
used to describe their measurements? (A) Imprecise and inaccurate, (B)
precise and inaccurate, (C) imprecise and accurate, (D) precise and accurate.

To answer this question, we need to
understand the difference between precision and accuracy. First, let’s get rid of the answer
choices to get some screen space. Accuracy is how close a scientific
measurement is to the correct value. Precision is how close scientific
measurements are to each other. A dartboard is often used to
explain the difference between these two terms. The center of the dartboard
represents the correct value. If our aim is accurate and we throw
a dart at the dartboard, the dart will hit the center circle of the board. But if our aim is not accurate, the
dart will miss the center of the board.

Now let’s say we throw three darts
at the dartboard, one right after the other. One of them hits the target, but
the rest are scattered across the dartboard. Because these darts did not land
close to each other, our dart throwing was not precise. So we throw another three darts to
try to redeem ourselves, which all land in one corner of the dartboard. Because these three darts are close
together, this time our dart throwing was precise. Notice that these three darts that
were precise are nowhere near the center of the dartboard. So even though our dart throwing
was precise, it wasn’t accurate because the darts didn’t hit the center of the board
representing the correct value.

Our dart throwing might also be
accurate but imprecise if the darts all hit the center circle of the dartboard, but
they aren’t close together. Of course, the goal is to be both
accurate and precise; that is, we would like to have all of our darts hit the center
of the dartboard and be close together.

Now that we know the difference
between accuracy and precision, let’s return to the question. And the question tells us that
students are measuring mass with a malfunctioning balance that displays values that
are 40 percent too large. If the balance isn’t displaying the
correct value, there’s no way that measurements made with this balance can be
accurate. Next, the question tells us that
the students measure the mass of a heap of caustic soda 20 times. All 20 of the measurements are
between 100.1 and 100.3 grams. 20 measurements all within 0.2
grams of each other are very close together, so these measurements are very
precise.

So “Which combination of words
should be used to describe their measurements?” That is answer choice (B) precise
and inaccurate.