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Three students (A, B, and C) are asked to determine the volume of a sample of ethanol. Each student measures the volume three times with a graduated cylinder. The results in millilitres are: $\mathrm{A} (87.1,88.2,87.6)$$; \mathrm{B}(86.9,87.1,87.2) ; \mathrm{C}(87.6,,$ 87.8,87.9 ). The true volume is $87.0 \mathrm{mL} .$ Comment on the precision and the accuracy of each student's results.

The average value of $A$ is 87.63 which shows the result are not even precise nor accurate as mean value is not close to true one. Also the spread of the readings is greater than $\mathrm{B}$ and $\mathrm{C}$ average value of $\mathrm{B}$ is 87.06 which is close to true value hence more accurate. The spread of readings is 0.3 which is same as that of $C$, hence same precision as of $C .$ since the average value of $C$ is 87.76 hence it is not accurate as one as B. The most precise student were $\mathrm{B}$ and $\mathrm{C}$ but the most accurate one was B

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

Carleton College

Rice University

University of Kentucky

University of Toronto

Lectures

02:29

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications.

04:42

In chemistry and physics, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles and objects that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (known as phases) that are defined by various physical properties, such as state of matter, phase, shape, and density. The Standard Model of particle physics and the general theory of relativity describe fundamental particles and the fundamental forces acting between them that control the structure and dynamics of matter.

01:40

Three students (A, B, and …

02:44

01:50

04:20

02:22

Ethanol is the substance …

05:15

Draw a picture showing the…

01:43

Ethanol has a density of $…

clay. So this question is asking you to comment on the precision and accuracy of some students results that are given. We have three students A, B and C, and you have to compare it to the true volume, which is 87.0 milliliters. So how you determine whether something is precise, is is you take the measurements and then you find the rate, which means subtract the greatest values track the smallest value from the greatest value, and the larger that range is, the less precise that measurement is unless precise and measurements are because, um, precision is a measurement of how close the their values are. So if the range is larger than you have, the values were just not as close. Right? And if you want Teoh measure the accuracy of their measurements, then you just take the mean and then you compare it to the actual value, which is 87.0 no leaders. So for each of these students a, B and C, let's find the first the range and then the mean Okay, so for this 1st 1 we have, you can see our greatest values 88.2 so 88.2, minus the least value, which is 87.1. And that will be the range. So the Rangers gonna put our and you should get 1.1. Okay? And now let's find me. Which would be, which is the average so 87.1 plus 88.2 plus 87.6 divided by three? Because there are three measurements and you should get 87.6 three. Yeah. Now for the range of the 2nd 1 What's our greatest value here? It's 87.2 87.2, minus 86.9. So that's just 0.3. And our means should be just again. Some all three, then divided by three because there are three of them. So some that divided by three she got 87 0.0 seven for the last one was find the range 87.9 minus 87.6. And that will be also 0.3. So same range for these two. And then for the mean we do the same thing again. Had them all together. Divide by three and we get it. 87 17 seven. Right. So, um, now we can see. Let's let's just look at precision first, right? Um, as you can see, the least precise measurement of these three by just by looking at the ranges here is eight because the range is the largest. So the measurements are much more spread out, whereas for B and C, their their their range is only a 0.3 for both of them. So they're only spread within a range of 0.3. So B and C are equally precise, but a is the is the least precise. So if we're gonna put a ranking of, like, precision here at the bottom, it would be, um, be equals, See greater than a Okay. Okay. Um and Alice, look at the accuracy at the meat. So for this one is pretty simple, um, or you do it. Just look at which one is closest, right? Which one is closest to 87? The actual value and you can see that be, which is 87.7 is closest, and the second closes a and then the last one is also on and then see is the least close. So if we're trying to do an accuracy. Just gonna put you for accuracy. It would be, um, be greater. That a greater than see. Okay. So, yeah, that's pretty much it for this question. Uh, my hope that you can understand is help you understand precision and accuracy a little bit more because they're both very, very important in chemistry in just math in general, Just science. So, yeah. Thank you for listening.

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