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Jackson $\qquad$ Washington $\qquad$ King170, 165, 140, 188, 195 $\qquad$ 144, 177, 215, 225, 197 $\qquad$ 166, 175, 196, 206, 219

Find the standard deviation of the weights for Washington High.

37.617

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

Oregon State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

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all right. So for number 28 we are moving on to the Washington weights that we need to find the the Well. First of all, we're finding the standard deviation officially. But in order find standard deviation. You need to be able to calculate the variation. And before you confined variation, you need to find the mean. So we're going to add up all those numbers, all those weights, and divide by the number of weights in that list. And there's five. So I've got 1 44 plus 1 77 plus 2 15 plus 2 25 plus 1 97 You're adding up all those numbers and you're going to get 9 58 And you needed a divide that by five, and you get 1 91.6 So step one is that we found the X bar the mean, and we're going to use that 1 91.6 several times in a step, too. So Step two has a little minor parts to it. It's getting the variation. So the first thing we're gonna do is take all the numbers on our list. The 1 44 all the way down to the 1 97 and subtract our average. But to recall average was 1 91.6 So we're gonna write in 1 44 minus 1 91.61 91.6 And he's gonna keep repeating up following a pattern. Um, because that is part of this Ramiele, okay? And so our goal is to subtract, and then two square these and we're gonna put those answers here, so I'm gonna dio 1 44 minus 1 91.6 and you do get a negative number. But remember, when you square a negative number, it's going to become positives. Always get a positive answer here. So you're going to get 2265 0.76 Then we're gonna do 1 77 minus 1 91.6 Get a negative, but we're gonna square it. Do not forget to square. And then you get to 13 point scene. I'm gonna do to 15 minus 1 91.6 23.4 But then remember to square it and that's going to give us 5 47.56 then to 25 minus 1 91.6 is 33.4. We square that and we get 1115.56. And lastly we do 1 97 minus 1 91.6 We get 5.4 square that we get 29 point 16. So with thes five numbers that we just got, we are ready to figure out what the variation is and pick out the variation. We're gonna take these numbers, and we're going to find the average or the mean of those numbers. So that means we add up all the numbers, all five members and divide by five. So I'm gonna take 2265.76 Add to 13 to 13.16 plus 5 47.56 plus 1115 0.56 plus 29.16 And when I adul five members up, I get 44,171 50.2. I needed I that by five. And what that gets us as a final answer will be our variants. So are variants is 8 34.24 and we are almost in the clear. So the last things that three is to actually get the standard deviation little bowl of a problem. So it turns out that the standard deviation is ever the square root of our variance. Waas. If I have square root, my vary, it's 8 34.24 and I around to the nearest 10th. That's going to be my standard deviations on the square root, 834.24 and I get 28.9. Approximately. That is our standard deviation for Washington's weights.

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