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Find the variance and standard deviation of each set of data to the nearest tenth.{5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}

$\sigma^{2}=1.6$$\sigma=1.3$

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

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

10:13

Find the variance and stan…

05:01

04:57

04:43

05:51

06:15

07:42

01:54

Find the mean and the stan…

05:50

04:14

00:50

03:27

02:13

Find the range and standar…

04:07

The given values represent…

02:23

02:11

00:36

02:17

Find the range, interquart…

01:03

the given values represent…

03:03

Okay, so remember, 70 to find the variance, this dinner deviation. And so we're gonna do that by finding the mean first. So that's when you add up all of these numbers and you're given lists and divide by the amount in the list. And it turns out that they're 16 in this list. So we'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'll get us 98 and then you do 98. Divided by 16 hour average is 6.125 now, honestly, it's exactly 6.125 But for the sake of room, I'm gonna go ahead and just rattle nearest 10th so we'll call it 6.1. Okay, so we're going to use that 6.1 quite a bit when we're trying to find the variance. The variance is when you'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're gonna get for all of the numbers of the list. So again, our mean is about 6.1, and we're gonna just rewrite that 6.1 over and over again. It gets to be a little tedious in this part, but it's very repetitive, so luckily, it's not too bad. All right, so we're ready to subtract and then remember were squaring because we cannot have a negative number. We're doing variance rescinded aviation. So when you get a negative, when you do like five minus 6.1, for example, you're gonna get a negative 1.1. But when you square it, it becomes positive. So that'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'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're gonna do six minus 6.1 and square yet 0.1 And that'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'll be the case for the others. Six. I'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'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'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't run the mean So I read it to me and I got 1.5. If you don't run the mean you bet 1.6. So the official answer is probably 1.6. But if you'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'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'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.

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