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Find the variance and standard deviation of each set of data to the nearest tenth.{400, 300, 325, 275, 425, 375, 350}

variance($\sigma^{2})=2500$standard deviagtion($\sigma)=50$

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

McMaster University

Lectures

01:32

In mathematics, the absolu…

01:11

07:42

Find the variance and stan…

05:50

04:43

10:13

05:51

06:15

04:57

05:01

06:42

00:50

Find the mean and the stan…

All right, remember, Six We need to find the variance in the Sudan deviation. So our first step whenever waiting to do that is to find the mean or the average we call that expert for short of the lists of given number. So this list has seven numbers, so we're going to be adding up all those numbers and dividing by seven. So I'm gonna take a calculator and add up the 400 plus 300 plus 3 25 plus 2 75 plus for 25 plus 3 75 plus 3 50 and we get 24 50 and rendered by that baseman, and we get exactly 350 as our average. So the average is very important because it gets used a lot in the second step. So our second step is to actually go ahead and find the variance. The variance is found by subtracting are mean from all of the numbers in the list. So they're seven overs and list. We're going to subtract all the numbers minus our 3 50 and then we need a square it because we're going to make sure we keep our various inter segregation positive. So you do 400 minus 3 50 and so on and so forth. So our again, our mean gets used a lot in a second step of the problem, which is OK, so we're just gonna be a lot of subtracting and squaring at this point. So 400 minus 3 50 is 50 50 squared is 2500 300. Ministry 50 is also technically 50 squared. So that's also 2500. Who ever So that look nicer. Great. One e 500. Ah, 3 25 minus 3 50 is 25. So we're 25 squared and we get 6 25 okay to 75 minus 3 50 is going to be negative. 75. But of course, when we swear we've become positive. So it's gonna be 56 25 4 25 minus 3 50 is 75. So if I've squared again that we just did this baby, that 56 25 again. Okay, 3 75 minus 3 50 is 25. Whenever I swear it is 6 25 and then there shooting mostly 50. That's an easy one. That zero in zero spurt zero So our last up to five variants is to add up all the person our boxes and find the mean of and that will be our variance. I'm gonna take 2500 plus 2500 plus 6 25 plus 56 25 36 25 plus 6 25 And we get 17,500 and then we divide by seven because there were seven items in the list and are mean or variance, rather is going to be 2500. So most the time you get a nice number here. Sometimes you have to brown there's tens of necessary, um, and then to get senator vacation because that was also part of the directions. You have to square root that now likely for us, the square root of 2500 ends up being a nice, easy number. It ends up being exactly 50. Sometimes you get a decimal most the time you get it s more other, and he'd have to round. But this time it's a nice hole number. Answer for number six

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