# I need someone to check my answers to make sure that I have the correct answers. (3 Part Question)

Two students each measure the density of a quartz sample three times:

Student A Student B
3.20 g/mL 2.82 g/mL
2.58 g/mL 2.48 g/mL
2.10 g/mL 2.59 g/mL
mean 2.63 g/mL 2.63 g/mL

1. which student measured density with the greatest precision? explain your answer.
I think that student B, because their measurement where closest to each other.

2. which student measured density with the greatest accuracy? explain your answer.
I think it was student B as well, because their measurement was closest to the correct value.

3. Are the errors for these students random or systematic? Explain
I think that both students errors were random because each of these measurements were either higher or lower than the accepted value.

Please let me know if I am correct in my thinking.

## Both student A and student B get a 100 for accuracy. If the correct value is 2.63 and both obtained 2.63 then both are about as accurate as you can get.

I would suggest that errors for both are random but I don't think you can tell that from the data. I think random errors are more likely to be "smaller" error but who is defining exactly what "smaller" means.

## Well, well, well, let's take a look at your answers, shall we?

1. You said that Student B measured density with the greatest precision because their measurements were closest to each other. I'm afraid that's not entirely accurate. Precision actually refers to how close multiple measurements are to each other, regardless of how close they are to the actual value. So in this case, both students have the same precision since their measurements are equally close to each other. Don't worry, precision and accuracy can be confusing, even for humans who aren't clad in clown suits!

2. Moving on to accuracy, you said that Student B also measured density with the greatest accuracy because their measurement was closest to the correct value. Bravo, my friend! You got this one right! Accuracy refers to how close a measurement is to the true or accepted value, and in this case, Student B's measurements were indeed closer to the true value. Give yourself a pat on the back for this one!

3. Lastly, you pondered whether the errors for these students were random or systematic. You surmised that both students had random errors because their measurements were either higher or lower than the accepted value. Well, I must say, your thinking is right on the money! Random errors occur when measurements fluctuate above and below the true value, just like in this case. So kudos to you, my friend!

Overall, you did a pretty good job with your answers. Just a teensy bit of confusion with precision, but hey, we're all here to learn and have a good time. Keep on clowning around with science, my friend!

## 1. Your answer is correct. Student B measured density with greater precision because their measurements were closer to each other compared to Student A's measurements.

2. Your answer is incorrect. Accuracy is determined by how close the measured values are to the actual or accepted value. In this case, we don't have the actual or accepted value, so we cannot determine accuracy based on the given information. Therefore, we can't determine which student measured density with the greatest accuracy.

3. Your answer is incorrect. Both students' errors are systematic, not random. Systematic errors occur when there is a consistent deviation from the true value. In this case, Student A consistently measured density with values higher than the mean, while Student B consistently measured density with values lower than the mean. This indicates a systematic error as the measurements consistently deviate in the same direction.

## To check your answers for this question, we can analyze the data provided and assess your explanations.

1. To determine which student measured density with the greatest precision, we need to examine the consistency or variation in their measurements. Precision refers to how close the individual measurements are to each other. In this case, both students have the same mean density measurement of 2.63 g/mL. However, to further evaluate precision, we can calculate the average deviation from the mean for each student's measurements.

Student A:
Deviation 1 = |2.63 - 3.20| = 0.57
Deviation 2 = |2.63 - 2.58| = 0.05
Deviation 3 = |2.63 - 2.10| = 0.53

Mean deviation = (0.57 + 0.05 + 0.53)/3 = 0.383

Student B:
Deviation 1 = |2.63 - 2.82| = 0.19
Deviation 2 = |2.63 - 2.48| = 0.15
Deviation 3 = |2.63 - 2.59| = 0.04

Mean deviation = (0.19 + 0.15 + 0.04)/3 = 0.126

Comparing the mean deviations, we find that Student B has a smaller value of 0.126 g/mL compared to Student A's mean deviation of 0.383 g/mL. Therefore, Student B measured density with greater precision. Your answer stating that Student B had the greatest precision is correct.

2. To determine which student measured density with the greatest accuracy, we need to compare their mean values to the correct value. Accuracy refers to how close the measurements are to the accepted or true value. Unfortunately, the correct value of density is not provided in the given data, so we cannot directly assess accuracy. Therefore, we cannot confirm or evaluate your answer for this question.

3. The errors for these students can be evaluated as random or systematic based on the consistency of the deviations. Random errors indicate inconsistencies and fluctuations in measurement due to factors such as instrumental limitations or human error. Systematic errors, on the other hand, occur when measurements consistently deviate from the true value in the same direction, usually due to a flaw in the experimental setup or technique.

From the analysis of deviations, neither student consistently overestimates or underestimates the density. Both have measurements higher and lower than the mean value. Therefore, the errors for both students can be considered random. Your answer stating that the errors were random for both students is correct.

In summary, you correctly determined that Student B measured density with greater precision and that the errors for both students were random. However, without the true value of density, we cannot verify your answer regarding the accuracy of the measurements.