Video: Describing the Accuracy and Precision of a Set of 3 Data Points Given the Average Value of the Set

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 _. [A] Not accurate and not precise [B] Accurate but not precise [C] Not accurate but precise [D] Accurate and precise [E] Accurate and precise but unreliable

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Video Transcript

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 results.

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 obtained.

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.

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