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Stem Leaf5 $\qquad$ 7 7 7 8 96 $\qquad$ 3 4 5 5 6 77 $\qquad$ 2 3 4 5 6 $\qquad$ 6 \ 3 = 63

$\approx 6.60$

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

Campbell University

McMaster University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

12:21

Stem $\qquad$ Leaf4 $\…

06:32

Construct a stem-and-leaf …

00:40

Divide.$$\frac{3}{…

00:31

Divide.$$\frac{6}{…

02:08

Divide.$$7 6 \longdiv …

01:07

01:58

$5 \frac{5}{6}+3 \frac{5}{…

03:44

Subtract.$$7 \frac{7}{…

01:21

Divide. $$\frac{\frac{6 s-…

00:48

Divide.$$2 1 4 \enclos…

All right. So remember, 13 were asked to find the standard deviation, but Nor to find the center deviation, we're gonna have to calculate the variance. And we need mean the average of our list given in order to do any of that. So first of where to were given a stem and leaf plot. And, um, it's just there to kind of have everything be there for you. Organized in order from smallest to largest. But you're gonna have to rewrite everything out. Um, set where you can kind of have everything listed out, um, to be able to find the meat. So first things first, you define the mean of the of the list. And so that's when you add up all the numbers and then you divide by, however, much is in the list. So we're going to do that real quick by adding it. 57 last 57 plus 57 plus with the eight plus 59 plus 63 64 plus 65 65 66 67 plus 7 2% agree with 4 75 76 So there I get a total of 1000 48 there were 16 numbers in the list. So our X bar, which means means or average, is going to end up being 65.5. So that's exactly 65.5. And so now we're gonna be test with is using that mean to calculate the variants? So you're going to take all the numbers in your list and they're going, though basically, rewrite them all out in a steptoe, find the variance So it's It's a little bit easier if you kind of follow a method. So eventually you're gonna be subtracting your list items minus your average as a new square. That's that way. You can always end up with positives. So, um, just for sake of keeping things orderly, I'm going to rewrite the the items out from the list, and then everything is gonna be getting sidetracked by 65.5. So for the sake of time I write down like that, there's an air of there, and I'm gonna put parentheses around these because that shows that we're gonna do subtraction first, According Toa, please excuse My dear Aunt Sally, a pen dos lord of operations. Whichever way you call it all right. And then we got to keep going with the rest of the list. So we've got a second column here, will be doing the same thing and so on. So we've got 60 for next have got 60 60 to 65 every 5 56 in the 67. So that's right. The minuses. And then again, for the sake of time, going to straw narrow down that that is gonna be a repeated situation. We're gonna square Well, that and then we had the ones in the seventies, so we had 70 to We have 73. 74 were 75 million facility sits not. And then remember, we're attracting the average and then square. Okay, so let's get that accomplish. Will use a dominating the text box to be ableto right in all these. Good. That's gonna hopefully help save some of the room here cause it is a little bit space usage. Move this of over todo just for the sake of keeping things orderly. Yeah, a little bit better That way. This Colin isn't all smushed. Okay? What if we need to cut so 57 I minus 65.5 and we're square that and you get 72 0.25 when you skirts of 72.25 Then you've got 57 minus 65.5, and you square that we get a positive Oops, that's another 57. So it's the same. It's the same thing. 72.25 72.25 and then our down under us up the new 58 minus 65.5. And risk where? That and we get 56 0.25 59 minus 65.5 squared gets us 42 point too far. Okay, so now we're ready for this one 63 line of 55.5 and we square that it's going to equal 6.25 64 months. 65.5 squared gets us equal toe to point to fuck 65. Last 65.5 is 1/2 square. The half get point 25 and that's gonna also be a 0.25 It was the same number 66 minus 65.5 will also be 0.5 squared. So that's another 0.25 and then 67 minus 65.5 squared there is too 0.25 Now I live. He's over. Just just imagine so that when we know we can fit everything. Okay, so 70 to minus 65.5 and squared is gonna be 42 0.25 73 minus 65.5 squared. It's US 56.2 five 74 minus 65.5 squared. It's us, uh, 72 0.25 75 months. 65.5 is the important five squared is gonna guess 90.25 and our last one 76 minus 65.5 is temper. Five squared is 110.25 Okay, so we have all these numbers now that I just typed out, and those numbers need to be added up and divided out by 17. Gonna find the variation of this and the variation is the average of all those numbers that we just captain. So I need to add up 72.25 plus 72.25 plus 72.2 sides plus 56.25 most 42.25 plus 6.25 plus 2.25 was 25.5 plus 25 plus 2.25 plus 42.25 plus 26.2 five plus 7 2.25 plus 90 0.25 less 110.25 We added all those up to get 6 98 and remember there were 16 items on our list. So to 6 98 divided by 16 and you're gonna get a pump, you're gonna get exactly ah 43.625 in order to get the standard deviation, the standard deviation. Who's end up being the square root of that variation that we just rounds. Of the 40 3.6 to 5 rounded to the nearest tents, it is going to be 6.6 approximately

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