jackson-qquad-washington-qquad-king-170-165-140-188-195-qquad-144-177-215-225-197-qquad-166-175-19-2

Question

Jackson $\qquad$ Washington $\qquad$ King
170, 165, 140, 188, 195 $\qquad$ 144, 177, 215, 225, 197 $\qquad$ 166, 175, 196, 206, 219

Find the standard deviation of the weights for Washington High.

Trinity Steen · Accepted Answer

all right. So for number 28 we are moving on to the Washington weights that we need to find the the Well. First of all, we&#x27;re finding the standard deviation officially. But in order find standard deviation. You need to be able to calculate the variation. And before you confined variation, you need to find the mean. So we&#x27;re going to add up all those numbers, all those weights, and divide by the number of weights in that list. And there&#x27;s five. So I&#x27;ve got 1 44 plus 1 77 plus 2 15 plus 2 25 plus 1 97 You&#x27;re adding up all those numbers and you&#x27;re going to get 9 58 And you needed a divide that by five, and you get 1 91.6 So step one is that we found the X bar the mean, and we&#x27;re going to use that 1 91.6 several times in a step, too. So Step two has a little minor parts to it. It&#x27;s getting the variation. So the first thing we&#x27;re gonna do is take all the numbers on our list. The 1 44 all the way down to the 1 97 and subtract our average. But to recall average was 1 91.6 So we&#x27;re gonna write in 1 44 minus 1 91.61 91.6 And he&#x27;s gonna keep repeating up following a pattern. Um, because that is part of this Ramiele, okay? And so our goal is to subtract, and then two square these and we&#x27;re gonna put those answers here, so I&#x27;m gonna dio 1 44 minus 1 91.6 and you do get a negative number. But remember, when you square a negative number, it&#x27;s going to become positives. Always get a positive answer here. So you&#x27;re going to get 2265 0.76 Then we&#x27;re gonna do 1 77 minus 1 91.6 Get a negative, but we&#x27;re gonna square it. Do not forget to square. And then you get to 13 point scene. I&#x27;m gonna do to 15 minus 1 91.6 23.4 But then remember to square it and that&#x27;s going to give us 5 47.56 then to 25 minus 1 91.6 is 33.4. We square that and we get 1115.56. And lastly we do 1 97 minus 1 91.6 We get 5.4 square that we get 29 point 16. So with thes five numbers that we just got, we are ready to figure out what the variation is and pick out the variation. We&#x27;re gonna take these numbers, and we&#x27;re going to find the average or the mean of those numbers. So that means we add up all the numbers, all five members and divide by five. So I&#x27;m gonna take 2265.76 Add to 13 to 13.16 plus 5 47.56 plus 1115 0.56 plus 29.16 And when I adul five members up, I get 44,171 50.2. I needed I that by five. And what that gets us as a final answer will be our variants. So are variants is 8 34.24 and we are almost in the clear. So the last things that three is to actually get the standard deviation little bowl of a problem. So it turns out that the standard deviation is ever the square root of our variance. Waas. If I have square root, my vary, it&#x27;s 8 34.24 and I around to the nearest 10th. That&#x27;s going to be my standard deviations on the square root, 834.24 and I get 28.9. Approximately. That is our standard deviation for Washington&#x27;s weights.

Trinity Steen · Answer

All right. So for number 29 that we need to be able to figure out the king weight average, Uh, and soon aviation. And so we&#x27;re going to add up all five of these numbers of weights of people playing football players, I believe. And, um, we&#x27;re going to eventually be able to calculate this inner deviation. So it&#x27;s a three step process. Step one is gonna be fine. The mean the X bar cause we&#x27;re gonna need that number when we&#x27;re plugging in to find the variation. So when you add up all these numbers, the 1 66 plus 1 75 plus 1 96 plus 2 +06 plus +219 and we get 9 62 and we&#x27;re gonna divide that by five, and we&#x27;re going to end up getting 1 92.4 So our X bar, the 1 92.4 is going to be a part of our various formula. So step two is get variation. And so, um, four 1 92.4 is going to be subtracted from all of the five numbers on our list. So 1 92.4 is going to go here, and you&#x27;re going to repeat that number for all five numbers. Hey, more. All right, so on our calculators were going to do 1 66 minus 1 92.4 And when you get a negative number, remember that you are going to be squaring this eventually. And that&#x27;s what&#x27;s gonna get written down here. So we&#x27;re gonna subtract and then square. Remember that negatives when they get scared, become positives. So 1 66 minus 1 92.4 is negative, 26.4. But when we swear that that&#x27;s 6 96.96 so that&#x27;s gonna go right here. 6 96 0.96 Then we&#x27;re going to do 1 75 minus 1 92.4 and we get negative. 17.41 square that, and we&#x27;re gonna get free 02 0.76 We&#x27;re gonna do 1 96 minus 1 92.4 We get 3.6 and we swear that and we get 12.96 then 206 minus 1 92.4 is 13.6. We square that we get 1 84 0.96 2 19 minus 1 92.4 is 26.6 were to swear that we get set 7.56 So those five numbers represent the part of how to get the variance. But what we got to do now, uhm, is kind of a last sub step of step to to get the variants. And that&#x27;s take the average of these five numbers. So remember, for average or mean or X bar, we have to add up the numbers and about the number of items in the list. That&#x27;s five this time someone adds 6 96.96 plus 302.76 plus 12.96 plus 1 84.96 plus 707.56 Add up all those numbers and we get 19+05 0.2 and divide that number by five. And we&#x27;re gonna end up getting 381.4 So what has calculated was our variance, which is what you need in order to be able to do one last small step, Step three, and that&#x27;s going to be to calculate the standard deviation. So that was a point of this problem was to be able to get to the Syrian deviation. And it&#x27;s just a one last step situation, and that&#x27;s going to be taking the square root of areas that we just got. So we&#x27;re in a square root that three age, one point 04 and we&#x27;re gonna round of the nearest 10th and that will be our final answers. A square root, the 3 81.4 and I&#x27;m going to get approximately 19 point five as my standard deviation.

Trinity Steen · Answer

already. So for number 27 were asked to find the Senate deviation of the Jackson Ah, high schools, weights from a football team. And so we&#x27;re going to have to first of all, find X bar the main because you&#x27;re in order to tactics, Aaron. Deviation, unifying, variance in order, find variance, unifying the average. So it&#x27;s kind of those domino effects. So we&#x27;re going to add up all those numbers 1 70 So we&#x27;re going to add up all numbers and divide by five. So we&#x27;ll add up together. 1 70 plus 1 65 plus 1 40 plus 1 88 plus 1 95 And we get 8 58 we have to divide by five. And I get 1 71.6 Exactly. So we&#x27;re going to now take that 1 71.6 and we&#x27;re going to use that to get the variation. So Variation is taking all five numbers and that list it&#x27;s attracting the mean for each of them. So that&#x27;s gonna be our first step. Step to a of the variation situation. So 1 70 1.61 71.6 they&#x27;re all gonna be building with the same number here, so it kind of follows a pattern. All right, so we&#x27;re gonna go ahead and do 1 70 minus 1 71.6 and then go ahead and square. Now, remember, if you get a negative number when you square a negative or when you square a positive, it will always be positive. So don&#x27;t be fooled by your calculator if you forget to do ah, parentheses around that square squaring situation. So you get to 0.56 and that&#x27;s after doing the square. Do you know for you to square? We&#x27;re gonna do 1 65 minus 1 71.6 and you&#x27;re gonna square it and you&#x27;re going to get 43.56 We&#x27;re gonna dio 1 40 minus 1 71.6 and square it. We get a big number 9 98 0.5 six. We&#x27;re gonna dio 1 88 minus 1 71.6 16.4 gets squared and we get to 68.96 1 95 minus 1 71.6 is equal to 20. We scored 23 points over then you swear it and you get 5 47 0.56 Alrighty. So now what we want to dio with our red numbers is move on to what I call step to be. And that means we&#x27;re going to average up thes numbers. Take the average of these numbers. So that means we add up the numbers and divide by five again because there&#x27;s five numbers in the list, so I&#x27;m gonna add up 2.56 plus 43.56 plus 9 98.56 plus 2 68.96 plus 5 47.56 out of those numbers and we get 18. 61 point to divide up by fine. And we get 3 27.24 So this right here is what we call the various. And in order to get our sooner deviation, we have to do one last thing and it doesn&#x27;t take much effort. You&#x27;re going to for, like, all set three. We&#x27;re going to get the standard deviation, which is our goal of this problem. And that&#x27;s by square rooting the variance. So we&#x27;re gonna square root 3 27 0.24 and around the nearest 10th on that. So you square root 372.24 you&#x27;re gonna get 19.3. And that, my friends, is your final answer. The standard deviation.

Trinity Steen · Answer

Okay. So for number four, we need to find the variance and standard deviation of the given list. And so the list goes from 3 21 goes in order, um, up until 3 30 So by accounting that out, that is 10 numbers. So the first thing we need to do whatever you&#x27;re finding very interested in aviation is to find the meat the X bar. So we&#x27;re going to make sure that whenever we add up all those numbers that we divide by 10 because there&#x27;s 10 numbers in that list, So we&#x27;re gonna go ahead and add up. 3 21 plus 3 22 plus 3 23 plus 3 24 plus 3 25 plus 3 26 plus 3 27 plus 3 28 plus 3 29 plus 3 30 And we get 3000 255. Okay. And then when you divide by 10 that&#x27;s gonna get us 3 25.5 And so we definitely are. Could be using that average quite often. And step two because the pub Aaron&#x27;s is your turn to see how first put out your mean is away from the numbers in the list. So I&#x27;m going to go ahead and we&#x27;re going to be taking all the numbers in our list. And we do each of them subtracted by the mean. So I&#x27;m gonna be rewriting three or 5.5 pretty often. Here, it&#x27;s clean. There we go. Sometimes the stylist has its own mind, I swear. Ah, it&#x27;s a 3 25.53 25.5 the 5.5. And this is a great way to help keep yourself organized the way that this is kind of set up. It&#x27;s a great way to show your work, because I imagine that is something you might have to be doing. Obviously, if you are allowed used technology and you were taught to use the technology methods, then feel free to do that as well. Just to build a check. Your word. Nothing wrong with verifying about the right answer. Okay. All right. So we&#x27;re gonna be subtracting. I&#x27;m gonna be swearing now. The reason why we square is because sometimes you&#x27;re gonna end up with a negative difference, and we want to always keep very insistent deviation positive. So by squaring it that will all ultimately always fix any negative. You might get somewhere, do 3 21 minus 3 25.5 And I get negative. 4.5. We&#x27;re gonna square that. And that&#x27;s going to get me 20.25 20.25 down. And then we&#x27;re gonna do 3 20 to minus 3 25.5 That&#x27;s gonna get us negative. 3.5 square that we get 12.25 3 23 minus 3 25.5 is 2.5 negative than you. Square that integrate at 6.25 Okay, so there, 24 minus 3 25 15 is in. The 1.5 squared gets, We get 2.25 and then we&#x27;re gonna have 0.5 getting squared. That&#x27;s me. 0.25 Right here. So then it pretty much because of how everything&#x27;s going. If I do 3 26 minus 3 25.5 that&#x27;s going to 0.5, squared 2nd 0.25 then this one is going to be two Point are 1.5 squared. That&#x27;s gonna get me the 2.25 So you could kind of see the pattern because it&#x27;s building back up on the positive sides. So we&#x27;re gonna get 6.25 here, we&#x27;re gonna get 12 0.25 and we&#x27;re going to get 20.25 and then And lastly, to get the variation is we take all the numbers that are now in my box, all 10 of them. I&#x27;m gonna add them up and abide to get the average, and that average ends up being our variance. So we&#x27;re going to do 20.25 plus 12.25 plus 6.25 plus 2.25 plus 0.25 plus 0.25 plus 2.256 45 plus 25 close 20.25 Add it all up. Get this 82.5. So 82.5 divided by 10 is going to be our variance and so are variants. Ends up Equalling eight 0.25 Gonna go ahead and put a circle around that and of course, we need to get the standard deviation as well. But luckily for us, that&#x27;s not a very big or tedious step. We&#x27;re gonna take whatever we just got in Step two, as are various 8.25 And we&#x27;re gonna swear route the 8.25 and we&#x27;re going to round to the nearest 10. So when we do that, you should be getting approximately you point nine as your standard deviation. Circle it and we&#x27;re done with number four.

Trinity Steen · Answer

All right, remember, Six We need to find the variance in the Sudan deviation. So our first step whenever waiting to do that is to find the mean or the average we call that expert for short of the lists of given number. So this list has seven numbers, so we&#x27;re going to be adding up all those numbers and dividing by seven. So I&#x27;m gonna take a calculator and add up the 400 plus 300 plus 3 25 plus 2 75 plus for 25 plus 3 75 plus 3 50 and we get 24 50 and rendered by that baseman, and we get exactly 350 as our average. So the average is very important because it gets used a lot in the second step. So our second step is to actually go ahead and find the variance. The variance is found by subtracting are mean from all of the numbers in the list. So they&#x27;re seven overs and list. We&#x27;re going to subtract all the numbers minus our 3 50 and then we need a square it because we&#x27;re going to make sure we keep our various inter segregation positive. So you do 400 minus 3 50 and so on and so forth. So our again, our mean gets used a lot in a second step of the problem, which is OK, so we&#x27;re just gonna be a lot of subtracting and squaring at this point. So 400 minus 3 50 is 50 50 squared is 2500 300. Ministry 50 is also technically 50 squared. So that&#x27;s also 2500. Who ever So that look nicer. Great. One e 500. Ah, 3 25 minus 3 50 is 25. So we&#x27;re 25 squared and we get 6 25 okay to 75 minus 3 50 is going to be negative. 75. But of course, when we swear we&#x27;ve become positive. So it&#x27;s gonna be 56 25 4 25 minus 3 50 is 75. So if I&#x27;ve squared again that we just did this baby, that 56 25 again. Okay, 3 75 minus 3 50 is 25. Whenever I swear it is 6 25 and then there shooting mostly 50. That&#x27;s an easy one. That zero in zero spurt zero So our last up to five variants is to add up all the person our boxes and find the mean of and that will be our variance. I&#x27;m gonna take 2500 plus 2500 plus 6 25 plus 56 25 36 25 plus 6 25 And we get 17,500 and then we divide by seven because there were seven items in the list and are mean or variance, rather is going to be 2500. So most the time you get a nice number here. Sometimes you have to brown there&#x27;s tens of necessary, um, and then to get senator vacation because that was also part of the directions. You have to square root that now likely for us, the square root of 2500 ends up being a nice, easy number. It ends up being exactly 50. Sometimes you get a decimal most the time you get it s more other, and he&#x27;d have to round. But this time it&#x27;s a nice hole number. Answer for number six

Trinity Steen · Answer

Okay, Dokey. So for number 10 we are finding the varying since then. Aviation. Before we can do that, we have toe average out all the numbers in our list. So there were 10 items or less. They are a little bit bigger of numbers, but we can still add up all those numbers and then divide by 10 to find the meaning. That&#x27;s gonna be our first test. So we&#x27;re going to add up all the numbers. 2 34 plus 3 45 plus 1 23 plus 3 68 plus 2 79 plus date, 76 plus 4 44 was 4 36 goes to 35 class, 333. Then I get 3000 693 and were dividing that by 10. So are mean is 3 69 0.3. So our task now is to use this mean that we just calculated and reuse it several times instead to in order to find the variance. So we&#x27;re gonna subtract 3 69.3 from all of our numbers on our list. As you can see, all those numbers were the ones in the list and we&#x27;re gonna subtract and then we&#x27;re gonna square And the reason why we square is so that we can keep our variance positive And our souls were singing deviation. So we&#x27;re just gonna writing 3 69.3 quite often. And if you want to, you could probably get away with kind of doing something like this to save time. Or, um, some things people do is like this little ah, these little quotation marks shapes to show that those for the state is the same thing. I honestly think if you draw a narrow down that it&#x27;s gonna be the same thing as a symbol on that could help you save some time. So we&#x27;re going to keep reusing 3 69.3 with our subtractions going to do to 34 minus 3 69.3 I&#x27;m going in a negative 1 35.3 But remember, have to square it so we can get a positive. That&#x27;s called me a bigger number. It&#x27;s gonna be 18,003 06 0.9 All right, so then we&#x27;re gonna do 3 45 minus 3 69.3 and 24.3 gets squared and we get 5 90 point for nine on. We&#x27;re gonna do 1 23 minus 3 69.3 and square that we get a big number. We can&#x27;t. 60,000 663.69 Then we have 3 68 minus 3 69.3 Relatively smaller this time for sure. 1.69 to 79 minus 3 69.3 and then square that you get 8000. 154.9 Okay, so 8 76 13 69.3 Square that and we get a very big number. We get 200 and 56,700 and 44 0.89 All right. 444 minus 3 69.3 square that you get 5000 580 0.9 for 4 56 minus 3 69.3 squared. It&#x27;s a 7000 516 0.89 2 35 mile s 3 69.3 I swear, is 18,000 36 might for nine. No, no. All right, 3 33 minus 3 69.3 is gonna get us 18 17 0.69 So all those numbers that we just got, we&#x27;re going to need to add up all of them and shift gears for thes numbers. We&#x27;re gonna go add up all of those numbers and find the average of that. And that will be the variance that we&#x27;re trying to find, so it&#x27;s gonna be able to typing. But it&#x27;s so worth it. It&#x27;s good practice. So 18,306 0.9 plus 590.49 plus 60,600 cc 3.69 plus 4.69 plus 8154 0.9 classed 256,744 0.89 plus 5580.9 plus 7516.89 Last 18,036 0.49 plus 1317 969 So you very decently sized number. Here we get 30 376,000 912.1. When you divide that by 10 years, move that decimal over. Once you&#x27;re going to get 37,000 691 0.2 rounder than years 10 then you square root that number, and that will be our standard deviation. So we want a circle that as a final answer, and there were a square root 37,000 690 1.2 you square root that answer square root that and we get 194.1 rounded to the nearest 10th for sanity mediation.

Problem

Jackson $\qquad$ Washington $\qquad$ King 170, 1…

Problem 28 Hard Difficulty

Jackson $\qquad$ Washington $\qquad$ King
170, 165, 140, 188, 195 $\qquad$ 144, 177, 215, 225, 197 $\qquad$ 166, 175, 196, 206, 219

Find the standard deviation of the weights for Washington High.

Answer

37.617

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