find-the-variance-and-standard-deviation-of-each-set-of-data-to-the-nearest-tenth-234-345-123-368-27

Question

Find the variance and standard deviation of each set of data to the nearest tenth.
{234, 345, 123, 368, 279, 876, 456, 235, 333, 444}

Trinity Steen · Accepted 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.

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

All right. So for number three, we are tasked with finding the variants and the standard deviation. So the variance is trying to figure out how far away things air spread out from the the mean on your list. So the first thing we need to do is find the me in order, be able to find the variance, and then ultimately, to be able to find this inter deviation. Remember, averages mean you add up all your numbers and then you divide by, however many numbers are on this list. So counting out from 48 all the way to the 37 I am counting 10. So that is the first thing we&#x27;re gonna be writing down is that we know that we have a ton. And so then we&#x27;re going to add up all these numbers. So we add up the 48 the 36 we&#x27;re gonna add 40 at 29 45 51 38 47 or at 39 37. And you should be getting 410. You divide Wharton divided by 10. And that&#x27;s gonna get me for you one as a mean Now we&#x27;re gonna be using that 41 quite often in depth to so step to a is getting the variants. So variances trying to figure out how spread out the mean is away from all the numbers in the list. So, as you can see, all of these numbers in front are the your list numbers, and we&#x27;re going to subtract your list numbers minus your means. So we&#x27;re gonna be rewriting 41 quite often here, and we&#x27;re going to be subtracting, and then I&#x27;m going to be squaring. And the reason why we square is so that way we can keep everything positive, because when you square a negative, you get a positive. And so that is the goal with finding various. All right, so we&#x27;re gonna do 48 minus 41 then square it. So 40 minutes 41 is seven squared. So we&#x27;re gonna do 49 year 36 minus 41 is five. So five squared is 25. Then we got one 29 take away. 41 is gonna be a negative 12. But remember, we&#x27;re square things. It&#x27;s become positive. 1 44 45 minus 41 is going to be 44 square to 16. 51 minutes. 41 is going to get us 100 when we square it. 38 minus 41 is 33 squared is 9 47 minus 41 a six X squared is 36. They&#x27;re nine minus 41 is 22 squared is for and 37 minutes 41 is four force word of 16. So moving on to the last part of fighting variances, we have all these numbers that are away from our mean and so and then squared. And so what we need to do now is lastly, to get the variance is we&#x27;re going to find the average of these 10 members. We&#x27;re gonna add up the nurse in the boxes here and here, and then we&#x27;re gonna divide by 10 to get the average, and that will finally answer the variance. So I&#x27;m going to do 49 plus 25 plus one plus 1 44 plus 16 plus 100 plus nine plus 36 plus four and plus 16. And we should get 400 So I&#x27;m gonna do 400 divided a 10. That&#x27;s exactly 40. And you&#x27;re going to want to circle that answer, because that is one of your two answers that you need to have for this problem. And then our final final thing is to get the center deviation. And luckily, I know it seems kind of tedious to get just to the variants, but left the sitter deviation, um, is not too much of an effort. So all you need to do to get the Senate evasion is square root, whatever. You just got in step two from the variance. So barbarians was 40 and about 9% of the time. Your square roots of these numbers will be, um, improper or irrational, rather. And so you&#x27;re gonna have to round the nearest tent. So scared of 40 is ah, 6.3. You&#x27;ll circle that or square that answer, and that will be it for number three.

Trinity Steen · Answer

that will always be your first steps. So you look at your list and you count how much you have in your lists. It turns out there&#x27;s nine. So remember the mean or the average is the same as adding up all of your numbers in your list and then dividing by night. So we&#x27;re gonna add up the 2.4 plus the 5.6 plus the one 0.9 plus the 7.1 plus the 4.3 plus the 2.7 and 4.6 and the 1.8 and the 2.4 and you get 32.8 already. And then you divide that by nine, and you get 3.6 officially rounds to the nearest 10th of 3.6. So you&#x27;re going to be using a 3.6 quite often in step two. So very of the seeing how far away your spread is from the mean So, um, we&#x27;re going to take all the numbers in the list all not above, and subtract the six, the 3.6. So I&#x27;m gonna write 2.4, minus 3.6 and 5.613 point six and noticed were squaring because when you subtract, sometimes you&#x27;re going to end up with negatives. But we can&#x27;t have negatives were doing very interesting a deviation. So we square that remember whenever you square negative, it becomes positive. So that&#x27;s why the squaring is going to happen eventually. Sort of subtract first, then square for all nine of these items in the list. So 2.4 minus 3.6 and then we square it get 1.44 Okay, 5.6 minus 3.6. And then I spirit we four. Okay, 1.99 of 3.6 and square it. We get 2.89 7.1. Line 3.6 and square it. You get 12.25 4.3 minus 3.6. Squared is 0.49 2.793 point six squared is pointing one 4.6. Lie in the 3.6 is one. So once weird is one as well. Uh, 1.8 my nephew 0.6. It&#x27;s negative. 1.8 weeks for that 3.24 and then 2.4 minus 3.6 square is the new one point for four. So the variance officially is the average of all of these numbers that we just calculated. So that means I&#x27;m gonna take all nine of these numbers and find the average of so we Adam and divide by nine to get and that will be our variants. So 1.44 plus four was 2.89 plus 12.25 plus point for nine plus 90.81 last one plus 3.24 plus 1.44 Get us 27. 56. Do not turn out nicely. Much weather. Okay. And then we divide that by nine. Okay, so we get 3.1 when we round to the nearest 10th which is what you&#x27;re gonna probably need to do on some of these. So 3.1 is one of our final answers. But then we take that 3.1, and we use that to get the sinner deviation as our finals at the standard deviation is very simple. You just take the square root of the number that we just got that 3.1 and you scared that and around the near sent, and you should get approximately 1.7. Now, if you square root the whole thing that&#x27;s from your calculator. It is 1.7. But if you just do the square root of 3.1, then that around a 1.8. So it just depends what you put in your calculator. So I would say, based on the fact that if we&#x27;re rounding to the nearest 10th here and then we input that into our sin deviation, that&#x27;s more likely going to work out of your final answer number. Sure, you&#x27;re a teacher, revealing it with that. It just depends on what they&#x27;re rounding. Specifications are, so make sure you ask your specific teacher.

Trinity Steen · Answer

but all right, so for number five, we need to find the variants listening deviation. Before we do that, we have to find the means of all of these numbers in the given list. So this list is pretty large. Turns out there are 17 numbers in this list. So what you&#x27;re gonna have to do then is add up all those numbers and then divide by 17. So we&#x27;re gonna do that first. Um, so we&#x27;re gonna have 43 plus 56 plus 78 plus 81 plus 47 plus 42 plus 34 plus 22 plus 78 close 98 plus 38 plus 46 plus 54 plus 67 plus 58 plus 92 plus 55 altogether gets us 989. So we&#x27;re gonna write down 989 here and we to divide by 17. He and we&#x27;re going to get a decimal that we&#x27;re gonna have two rounds that were in around the nearest town, so you should get 58.2 approximately. Now. This 58.2 this mean is very important because that&#x27;s how we could measure the spread or the variance from the mean. So we&#x27;re going to use Bean and bitterly suffuse all of these numbers in this list and subtract this number from the mean with the mean And then we got a square it. Now, the reason why we square everything is because we want to keep things positive so again, Army and is 58.2 and we&#x27;re going to reuse this number several times in this list of 58 point to 50 point there, 58.2, 58 0.2 stone. Yeah. I mean, is very important to get to use quite often in these problems. Hey, Stared. This is one of the longer ones because the list is so long not gonna have this long of a list. And if you have access to doing something with technology, like to be able to find this with technology and get your allows that that&#x27;s 100% okay. But that&#x27;s just how you show your work if you are required to. All right, so we&#x27;re gonna subtract and square, so really go ahead and go through the list and do that. So 43 on a 58.2 gets me a negative. But remember, when you square negative, you get a positive. So you should get to 31 0.4 for that 1st 1 56 minus 58.2 squared gets us 4.84 You&#x27;re OK. 78 minus 58.2 Squared 3 92.4 81 minus 58.2 Squared 5 19.84 47 minus 58.2 squared. Get this 1 25.44 40 to minus 58.2. Squared gets us to 62.44 and then ready for the next column. 34 minus 58.2. Squared gets us 5 85.64 20 to minus of the 8.2 on. Dsquared gets US 13. 10.44. It&#x27;s a bigger number. All right, 78 minus 58.2. Gives us 19.8 squared. It&#x27;s US 3 92.4 Okay, 98 minus 58.2 squared. It&#x27;s this 15 84. That&#x27;s a 12 0.4 All right. 38 minutes 58.2 squared. Get this. 408.4 46 minus 58.2. Gets a snake it of 12.2, but were squaring that we get a positive 1 48 0.84. Then 54 minus 58.2. Squared gets a 17.64 on this last call. Okay, 67 minus 58.2 is 8.8 and we square that 77.44 look a little nicer. 0.44 All right, 58 minus 58.2 squared. Get this point. 04 90 to minus 68.2 and then squared. Get this. 11. 42 point 11. 42 point for four. Your point for now. Okay. And then 55 minus 58.2 squared gets us 10.24 So after all that tedious work, I know that was a lot because our list was so big. Um, we&#x27;re going to need to actually get the variation. So we get the variation by taking all three numbers in these columns, and we&#x27;ll add them all up and find the average of that that was just the various. So it will take a little bit, but it will be fine. So we got to 31.4 plus four 0.84 plus 3 92.4 plus 5 19.84 plus 1 to 5.44 plus 262.44 plus 5 85.64 plus 13 10.44 plus 3 92.4 1584.4 plus 4 8.4 plus 1 48.84 plus 17.64 plus 77.44 plus 0.0 for plus 11. 42.44 This was before for and then last, but at least 10 0.24 We add all those up and we get a grand total of 7000 212.44 We divide by 17 and that will definitely to be rounded. It&#x27;s 424.3. We take that 424.3 and we need to now use that to get the standard deviation so the sooner deviation is always a square root of the variants that we just got. So we&#x27;re gonna square root the 4 24.3 and I think that look a little bit nicer. And then we get approximately 20.6 rounded to the nearest tense of make sure circle or square, your Final Two answers air the variance and the senior deviation as 20.6 for number five.

Problem

Find the variance and standard deviation of each …

Problem 10 Medium Difficulty

Find the variance and standard deviation of each set of data to the nearest tenth.
{234, 345, 123, 368, 279, 876, 456, 235, 333, 444}

Answer

$\sigma^{2}=37691.2$
$\sigma=194.1$

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$\sigma^{2}=37691.2$$\sigma=194.1$

Algebra

Catherine R.

Alayna H.

Kayleah T.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, HayekAlgebra

Catherine R.

Alayna H.

Kayleah T.

Kristen K.

$\sigma^{2}=37691.2$
$\sigma=194.1$

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Algebra