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Find the variance and standard deviation of each set of data to the nearest tenth.{321, 322, 323, 324, 325, 326, 327, 328, 329, 330}

8.25,2.9

Intro Stats / AP Statistics

Algebra

Chapter 12

Probability and Statistics

Section 6

Statistical Measures

Sampling and Data

The Normal Distribution

Introduction to Combinatorics and Probability

Missouri State University

Oregon State University

McMaster University

Baylor University

Lectures

01:32

In mathematics, the absolu…

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07:42

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04:14

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04:57

05:01

10:13

05:51

06:15

06:42

01:29

Find the mean and the stan…

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're finding very interested in aviation is to find the meat the X bar. So we're going to make sure that whenever we add up all those numbers that we divide by 10 because there's 10 numbers in that list, So we'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'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's is your turn to see how first put out your mean is away from the numbers in the list. So I'm going to go ahead and we're going to be taking all the numbers in our list. And we do each of them subtracted by the mean. So I'm gonna be rewriting three or 5.5 pretty often. Here, it's clean. There we go. Sometimes the stylist has its own mind, I swear. Ah, it'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'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're gonna be subtracting. I'm gonna be swearing now. The reason why we square is because sometimes you'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're gonna square that. And that's going to get me 20.25 20.25 down. And then we're gonna do 3 20 to minus 3 25.5 That'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're gonna have 0.5 getting squared. That's me. 0.25 Right here. So then it pretty much because of how everything's going. If I do 3 26 minus 3 25.5 that's going to 0.5, squared 2nd 0.25 then this one is going to be two Point are 1.5 squared. That's gonna get me the 2.25 So you could kind of see the pattern because it's building back up on the positive sides. So we're gonna get 6.25 here, we're gonna get 12 0.25 and we'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'm gonna add them up and abide to get the average, and that average ends up being our variance. So we'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's not a very big or tedious step. We're gonna take whatever we just got in Step two, as are various 8.25 And we're gonna swear route the 8.25 and we'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're done with number four.

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