find-the-variance-and-standard-deviation-of-each-set-of-data-to-the-nearest-tenth-24-56-19-71-43-27-

Question

Find the variance and standard deviation of each set of data to the nearest tenth.
{2.4, 5.6, 1.9, 7.1, 4.3, 2.7, 4.6, 1.8, 2.4}

Trinity Steen · Accepted 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

my numbers, and we need to be able to find the mean first. That&#x27;s always our first step in whatever we&#x27;re doing these sorts of problems. So I&#x27;m gonna go ahead and add up these numbers and then divide by nine because there&#x27;s nine items in the list someone do. 4.3 plus 6.4 plus two point nine plus 3.1 plus 8.7 plus 2.8 was 2.6 post one 0.9 plus seven point to get 40.9 on top. And then we&#x27;ll divide that by nine and we get 4.5, but four repeating. So where&#x27;s gets a 4.5 is our mean and we&#x27;re gonna be reusing that being a lot and step and step to to find the actual variance. So when everyone Nigerians, you&#x27;re taking all the numbers in your listen, subtracting them from the meat. So 4.5 So we&#x27;re gonna have 4.5 be written down quite a bit here, and this is a good way to show the work. It helps keep you organized and just let you take things step by step, which I&#x27;m sure your teacher would like to see now if they prefer. If they a rookie of using technology, then you know that&#x27;s also a great thing. I&#x27;ve been writing for points exception. It should be a 4.5 and I want to I four point fives. Okay, so we&#x27;ll subtract thes numbers and then we square them, though the reason when we swear them is because we need to keep them positive for variances in a deviation and so scoring a number. What it&#x27;s negative will always become positive. So 4.3 minus 4.5 and then we square that negative point to to become a point. 04 Write that down, then keep going. 6.4 minus 4.5 square the 1.9 and gets US three 0.61 2.9, minus 4.5. Native 1.6 and then we square it. We had a 2.56 3.1 last 4.5 negative. 1.4 squared gets us 1.96 8.7, minus 4.5 squared. It&#x27;s a 17 0.64 2.8, minus 4.5. Squared is two point night 3.6 minutes 4.5 We square the name of the point that he gets his 0.0.81 1.9 less Well, 0.5 square to get the 6.76 and 7.2 minus 4.5 squared. It&#x27;s a 7.29 Now wrap up the veer variance We need to take all the numbers we just found and add them up and face. We find the average of the of these nine numbers so I&#x27;m gonna take these nine numbers that we just got and I&#x27;m gonna find the mean and that will be variance So 0.4 plus 3.61 plus 2.56 plus 1.96 plus 17.64 plus 2.89 plus 0.81 plus 6.76 plus 7.29 get 43.56 and then we&#x27;re going to divide by nine. That gets us 4.84 Exactly. So you could say 4.4 or four point a that be fine. But whatever you say to Dio, you&#x27;re gonna have to square root that in order to get the sanity aviation. So you&#x27;re sitting deviations on with a square root of the variance. So wanna square root 4.84 and we get exactly two point to do that. All right, there&#x27;s or two answers number night.

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.

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

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 remember, 70 to find the variance, this dinner deviation. And so we&#x27;re gonna do that by finding the mean first. So that&#x27;s when you add up all of these numbers and you&#x27;re given lists and divide by the amount in the list. And it turns out that they&#x27;re 16 in this list. So we&#x27;re gonna go ahead and add up all these numbers real quick. Five plus four plus five plus five plus five plus five plus six plus six plus six plus six plus seven plus seven plus 7.7. Lucy was eight and nine. We&#x27;ll get us 98 and then you do 98. Divided by 16 hour average is 6.125 now, honestly, it&#x27;s exactly 6.125 But for the sake of room, I&#x27;m gonna go ahead and just rattle nearest 10th so we&#x27;ll call it 6.1. Okay, so we&#x27;re going to use that 6.1 quite a bit when we&#x27;re trying to find the variance. The variance is when you&#x27;re trying to see how far away from the mean your list items are from our and so we subtract the list item minus the mean and square it. So we&#x27;re gonna get for all of the numbers of the list. So again, our mean is about 6.1, and we&#x27;re gonna just rewrite that 6.1 over and over again. It gets to be a little tedious in this part, but it&#x27;s very repetitive, so luckily, it&#x27;s not too bad. All right, so we&#x27;re ready to subtract and then remember were squaring because we cannot have a negative number. We&#x27;re doing variance rescinded aviation. So when you get a negative, when you do like five minus 6.1, for example, you&#x27;re gonna get a negative 1.1. But when you square it, it becomes positive. So that&#x27;s good. 1.21 Oh, boy. Race that. Yeah, there were you. All right? So do four minus 6.1, and then we square that and we get 4.41 Okay, so we&#x27;re gonna do five minus 6.1. Swear it is going to get us 1.21 And then, since these air the same than these have to also be the same. So 5.1 point 211.21 and 1.21 They&#x27;re gonna do six minus 6.1 and square yet 0.1 And that&#x27;s going to point a one for thes other ones as well. Seven minus 6.1 is point nines. Where that you get 0.0.81 And that&#x27;ll be the case for the others. Six. I&#x27;m missing a seven. So good thing I caught that. Oh, was double check your numbers. Okay, so then get 0.81 here. Okay, so then we&#x27;ve got eight minus 6.1, 1.9 squared. Is this 3.61 and 99 A 6.1 is 2.9 and square that we get 8.41 So the final step in finding the variants remember fronting variants answered aviation. The final step to getting the variance is to take all the numbers in our list and add them up. If I mean so divided by 17 then So I&#x27;m gonna go and add 1.21 plus 4.41 plus 1.21 plus one to, um plus 1.21 plus 1.21 plus point. +01 plus 10.1 plus point award was pointing a one plus 0.81 plus 0.81 plus 0.81 point +81 plus three points, 3.61 plus 8.41 You get 25.76 So we got 25.76 and we divide that by 17 and we end up getting about 1.6. Now I did round, um, the mean if you don&#x27;t run the mean So I read it to me and I got 1.5. If you don&#x27;t run the mean you bet 1.6. So the official answer is probably 1.6. But if you&#x27;re close within 1/10 or so and it shows in your book that you had rounded your mean, then you are still fine. So either way, we&#x27;re gonna take whatever we get, as are various and me to go get the standard deviation. So we will accomplish getting standard deviation by square rooting whatever we got for the variant. So it was 1.6 or 1.5 gonna square root that and you&#x27;ll end up getting 1.2 or 1.3, depending on how you rounded with your me. And so there you have your mean and your variants for numbers number seven.

Problem

Find the variance and standard deviation of each …

Problem 8 Medium Difficulty

Find the variance and standard deviation of each set of data to the nearest tenth.
{2.4, 5.6, 1.9, 7.1, 4.3, 2.7, 4.6, 1.8, 2.4}

Answer

$\sigma^{2}=3.1$
$\sigma=1.8$

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

Algebra

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Anna Marie V.

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Absolute Value - Example 1

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$\sigma^{2}=3.1$$\sigma=1.8$

Algebra

Grace H.

Anna Marie V.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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

Grace H.

Anna Marie V.

Maria G.

Michael J.

$\sigma^{2}=3.1$
$\sigma=1.8$

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

Algebra