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Find the variance and standard deviation of each set of data to the nearest tenth.{4.3, 6.4, 2.9, 3.1, 8.7, 2.8, 3.6, 1.9, 7.2}

$\sigma^{2}=4.84$$\sigma=2.2$

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

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

05:01

Find the variance and stan…

10:13

04:43

07:42

05:50

06:42

06:15

05:51

00:50

Find the mean and the stan…

04:14

01:54

04:47

The given values represent…

01:29

00:45

02:13

Find the range and standar…

03:27

02:23

00:36

02:11

03:03

my numbers, and we need to be able to find the mean first. That's always our first step in whatever we're doing these sorts of problems. So I'm gonna go ahead and add up these numbers and then divide by nine because there'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'll divide that by nine and we get 4.5, but four repeating. So where's gets a 4.5 is our mean and we're gonna be reusing that being a lot and step and step to to find the actual variance. So when everyone Nigerians, you're taking all the numbers in your listen, subtracting them from the meat. So 4.5 So we'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'm sure your teacher would like to see now if they prefer. If they a rookie of using technology, then you know that's also a great thing. I've been writing for points exception. It should be a 4.5 and I want to I four point fives. Okay, so we'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'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'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'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'm gonna take these nine numbers that we just got and I'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'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're gonna have to square root that in order to get the sanity aviation. So you'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's or two answers number night.

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