So your research investigator and you want to hire a research assistant to help progress your investigations. You have three applicants, applicant 12 and three. And you give them a test in order to determine which one will be the best fit for your lab. This test involves transferring 100 and 50 micro leaders from ap 200 micro pipe it onto an analytical balance and they have to measure the weight of each of those drops to see how accurate they are to the target of 100 and fifty's or I guess would be zero point 15 g. And so we're going to look at how accurate and how precise there are. Three sets of measurements are. Each candidate was asked to replicate the procedure three times. Hence we have three measurements and this is the information we're going to use to annihilate analyze the candidates. So first we're going to start by just doing some basic statistics. We're going to look at the mean and standard deviation for each measurement produced by each of the three applicants. So essentially how we calculate the mean for each applicant is that we take the sum of each of their individual measurements, so the addition signs. So we take the sum of each of those three measurements for this first candidate. That will give us a value of 0.450 And now we're going to divide that by the total number of measurements, which is three, and that is going to produce a value of 0.150 So this is going to give us the average. Mhm Okay. And we're going to repeat that for each of these candidates. Were going to take this some of the measurements from applicant to we're going to divide those by three and that is going to produce an average of 0.1 five. So yeah, okay. Now we're going to do the same thing for applicant number three, we're going to add up each of these values, We're going to divide them by three and that's going to give us a value of zero point 148 667 But we're going to keep three significant figures because that's what we have here. 123 Mhm. And that's going to give us a standard. Sorry, an average of 0.14 nine. Sometimes it's good to keep an extra string of these numbers when you were doing further populations so we can get a more representative answer. But here are the three averages for each of the candidates. Now we're going to calculate the standard deviation. I'm going to just write out the basic formula for standard deviation. Standard deviation is just a measure of how much each of these individual values deviates from the average value. So the measurement would be. Standard deviation is equal to the square root of the sum of deviations and the deviation would be are mhm individual measurement minus r average, Mhm squared divided by our total number of measurements minus one. So we're going to do that formula for each of these candidates. So let's scroll down so we have some more space to work with. So for applicant one, a standard deviation for applicants, number one is going to equal this big the square root of our first measurement and I've written them here so we can quickly see them. Um 0.161 minus the average. Which we said was if we scroll up we can see it but it was 0.15 Mhm. Yeah, this wear that since it's some we're going to add and then we're going to our next measurement which was zero 0.147 minus our average of 0.15 squared plus our final measurement of 0.14 to minus 0.150 squared. Okay, I'm going to take these deviation squared and divide those by the total number of observations which we have three minus one. So that would be too and he punched out into our calculator. The standard deviation for candidate number one would give us a value of 0.0 nine eight five. If we keep it the same thing as it goes on a little bit more to like 50.98 4858 But we're going to keep our signature safeties, three significant figures. And now we're going to do the same standard deviation calculated calculations for applicant number two. To the standard deviation for applicant number two, let's see what color we had originally used. Radical Number two Mr Green. So we're going to take the square root of his first individual measurement. Mhm. So 0.158 minus his average. And his average was we said 0.157 minus 0.157 squared plus our second observed measurement for applicant to which is 0.156 minus 0.157 That was his average squared plus his final observation of zero point 157 minus his average of 0.157 squared. We're going to divide that by the total number of observations, three minus one, which would give us a value of two and then the tow the standard deviation. We punch that into the calculator. For applicant number two would be 0.100 Okay, now we're going to do the same formula for applicant number three. And let's just look at his average was we said 0.48667 We're just gonna keep that as we punch it in here. Yeah. And his color. I believe this blue. So the standard deviation for applicant number two is equal to you know what I just said that there's no confusion at an equal sign here to our first measured value for applicant number three is 0.14 three minus his average of 0.1 for eight 667 Or you could just say um 89 Where is gonna make it a little bit? Configure their distance for making allergic calculation. And we're gonna do the second observed average. Sorry, The second observed measurement of zero point 153 minus 0.14 8667 That's our average for applicant number three. And it's not reduced to any significant figures yet squared plus our final measurement for applicant number three of zero point 15 minus 0.1 four eight. And it would be that same number 667 I'm just going to put a little here to recreate that and that's going to be squared. Sorry, I ran out of space there. But when we punch that and just remember that this value here, this is the same value here. Okay, so when we punch this into a calculator, oops, we forgot one last part. We're going to divide that by the total number of observations which we have three measurements. We're going to divide. Subtract one from that, which will give us a two. We punch this into our calculator. It's going to give us a standard deviation of 0.5 one 316 And it goes on a little bit more, but we're just going to take the sig figs for that. So that's a three Sig figs. 0.51 three. Mhm. I'm sorry, that looks really bad right there to me. Rewrite that. 51 three. Okay, so now we have some numbers to work with here. And we're going to do a further calculation, we're going to look at percent accuracy. So percent accuracy. Okay, yeah, is essentially the observed average. So, you have observed average? Okay, okay. Oh, Bs are observed divided by our theoretical average times 100. That's a tease for theoretical. And in this case, we know that our theoretical value would be 0.150 because that's the amount that we wanted them to transfer. We know that the density of water is one gram per one and later squared. And so when we do that calculation essentially beat that, our theoretical value would be a 0.150 Or you can say 100 and 50 micro leaders. As long as we keep both of these in the same unit doesn't matter too much. Okay so we're going to calculate the percent accuracy for a candidate number one. So the accuracy for candidate number one, His observed average was 0.150 and our theoretical average was 10.150 We multiply that by 100 we know that this portion here becomes one times 100 equals 100%. And now when we do candidate number two, let me see what color. I think it was green. It's one double check. We do the accuracy for candidate number two. Excuse me. Let's redraw that. Their accuracy. Yeah. Oh candidate number two. We took his average of history measurements or her measurements. 0.15 seven divided by our theoretical average of 0.150 times 100. And the number that we get is 0.1. Sorry. Mhm. Do you erase some of this really quick? The number that we should get is 100 466 etcetera. Seven. Uh huh. Or we could rob for keeping with our six figs. We would say that this is 100 5% and out for candidate number three. We're going to take the his or her accuracy of Canada number three which there mean was 0.14 eight peel extra digits there just for this calculation divided by the theoretical average of 0.5 times 100. We put that into the calculator. That's going to give us a value of 99.111 There is 99.1%. Okay, so now we are going to rank our candidates, you know, based on their accuracy and accuracy is basically a measure of how close the observed measurements are to our theoretical measurement. So how close are each of these measurements to our desired measurement of 150. So let's see, let's rank them. The best one would be 100% which is candidate number one. So this candidate receives a ranking of first place. Yeah, there we go, number one. And um our next best measurement of percent accuracy would be candidate number three. So this candidate would receive second place and the worst of the three would be candidate number two. So they would get third place. And when we look up here at each of these candidates, in terms of standard deviation, which will help us see the the precision, which is essentially how close our each of these values to each other, so um how reproducible are there? Are they are getting the same types of results? So we're going to look for is the standard deviation that is closest to zero. So the one that is closest to zero out of all of these would be candidate number two. Yeah, the one that is the next best to be, the next smallest would be candidate number three mm and the next best after that would be candidate number four. Since this is our sorry, candidate number one. Since this is our largest standard deviation. So if we were to just chart out some of these rankings here, let's put candidate won candidate to and candidate three. So these are the candidates uh huh. Now if we rank them by open mhm accuracy and precision, let's look at um where candidate one ranks here, let's look at accuracy. So candidate one got a first ranking, candidate three got second ranking and candidate to got the third rankings. Let's just write that in here. Candidate one to calm the gold medal there. Candidate to received second place and candidate three received third place. I'm sorry, I just wrote that incorrectly. Let me write that again. That's why we always go back and check can it three. Candidate three actually received second place candidate to received third place according to our ranking there. Let's just double check that candidate one is first candidate to is in third place and candidate three is in second place. We determine this just based on how close each of these percent accuracy, these are 200%. Now, in terms of standard deviation or the measure of precision, candidate three was in second place, again, candidate to was in first place and candidate one was in third place, candidate to here to calm the gold medal, candidate number one to comb third place. Okay. And we determined these position based on um the size of the standard deviation, the smaller standard deviation, that means the less variance, which means more precise. And what we see here is that a negative number one toward well and accuracy, but they weren't very precise. So although they were close to the right answer, on average, they the results weren't very reproducible and that could be a very that could be a problem in the lab. Now, candidate number two was not very accurate, which is also a problem, but they had very high precision, which essentially translates as they were very good at getting the wrong answer, which is also not a good feature in the Laboratory of Research can remember three get pretty well with accuracy. They play second and they got about 99.1% and then candidate um number three in terms of precision came in second place. So they were they were average and I think that I would prefer to work with candidate number three because their accuracy was close to 100% was 99.1 and their precision was on was uh was ranked second. Um I wouldn't want to work with candidate one and two. As I mentioned before, candidate one wasn't very precise had the worst precision which is important in science. You want to be reproducible and then candidate number two was the least accurate. Which is also a problem. So we would go with candidate number three, candidate number three, you are hired