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Find the variance and standard deviation of each set of data to the nearest tenth.{234, 345, 123, 368, 279, 876, 456, 235, 333, 444}

$\sigma^{2}=37691.2$$\sigma=194.1$

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

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

05:50

Find the variance and stan…

04:14

04:43

05:01

10:13

04:57

05:51

06:15

06:42

01:29

Find the mean and the stan…

Okay, Dokey. So for number 10 we are finding the varying since then. Aviation. Before we can do that, we have toe average out all the numbers in our list. So there were 10 items or less. They are a little bit bigger of numbers, but we can still add up all those numbers and then divide by 10 to find the meaning. That's gonna be our first test. So we're going to add up all the numbers. 2 34 plus 3 45 plus 1 23 plus 3 68 plus 2 79 plus date, 76 plus 4 44 was 4 36 goes to 35 class, 333. Then I get 3000 693 and were dividing that by 10. So are mean is 3 69 0.3. So our task now is to use this mean that we just calculated and reuse it several times instead to in order to find the variance. So we're gonna subtract 3 69.3 from all of our numbers on our list. As you can see, all those numbers were the ones in the list and we're gonna subtract and then we're gonna square And the reason why we square is so that we can keep our variance positive And our souls were singing deviation. So we're just gonna writing 3 69.3 quite often. And if you want to, you could probably get away with kind of doing something like this to save time. Or, um, some things people do is like this little ah, these little quotation marks shapes to show that those for the state is the same thing. I honestly think if you draw a narrow down that it's gonna be the same thing as a symbol on that could help you save some time. So we're going to keep reusing 3 69.3 with our subtractions going to do to 34 minus 3 69.3 I'm going in a negative 1 35.3 But remember, have to square it so we can get a positive. That's called me a bigger number. It's gonna be 18,003 06 0.9 All right, so then we're gonna do 3 45 minus 3 69.3 and 24.3 gets squared and we get 5 90 point for nine on. We're gonna do 1 23 minus 3 69.3 and square that we get a big number. We can't. 60,000 663.69 Then we have 3 68 minus 3 69.3 Relatively smaller this time for sure. 1.69 to 79 minus 3 69.3 and then square that you get 8000. 154.9 Okay, so 8 76 13 69.3 Square that and we get a very big number. We get 200 and 56,700 and 44 0.89 All right. 444 minus 3 69.3 square that you get 5000 580 0.9 for 4 56 minus 3 69.3 squared. It's a 7000 516 0.89 2 35 mile s 3 69.3 I swear, is 18,000 36 might for nine. No, no. All right, 3 33 minus 3 69.3 is gonna get us 18 17 0.69 So all those numbers that we just got, we're going to need to add up all of them and shift gears for thes numbers. We're gonna go add up all of those numbers and find the average of that. And that will be the variance that we're trying to find, so it's gonna be able to typing. But it's so worth it. It's good practice. So 18,306 0.9 plus 590.49 plus 60,600 cc 3.69 plus 4.69 plus 8154 0.9 classed 256,744 0.89 plus 5580.9 plus 7516.89 Last 18,036 0.49 plus 1317 969 So you very decently sized number. Here we get 30 376,000 912.1. When you divide that by 10 years, move that decimal over. Once you're going to get 37,000 691 0.2 rounder than years 10 then you square root that number, and that will be our standard deviation. So we want a circle that as a final answer, and there were a square root 37,000 690 1.2 you square root that answer square root that and we get 194.1 rounded to the nearest 10th for sanity mediation.

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