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Find the variance and standard deviation of each set of data to the nearest tenth.{43, 56, 78, 81, 47, 42, 34, 22, 78, 98, 38, 46, 54, 67, 58, 92, 55}

$var=424.3$$Stdev=20.6$

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

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Campbell University

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In mathematics, the absolu…

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Find the variance and stan…

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00:50

Find the mean and the stan…

but all right, so for number five, we need to find the variants listening deviation. Before we do that, we have to find the means of all of these numbers in the given list. So this list is pretty large. Turns out there are 17 numbers in this list. So what you're gonna have to do then is add up all those numbers and then divide by 17. So we're gonna do that first. Um, so we're gonna have 43 plus 56 plus 78 plus 81 plus 47 plus 42 plus 34 plus 22 plus 78 close 98 plus 38 plus 46 plus 54 plus 67 plus 58 plus 92 plus 55 altogether gets us 989. So we're gonna write down 989 here and we to divide by 17. He and we're going to get a decimal that we're gonna have two rounds that were in around the nearest town, so you should get 58.2 approximately. Now. This 58.2 this mean is very important because that's how we could measure the spread or the variance from the mean. So we're going to use Bean and bitterly suffuse all of these numbers in this list and subtract this number from the mean with the mean And then we got a square it. Now, the reason why we square everything is because we want to keep things positive so again, Army and is 58.2 and we're going to reuse this number several times in this list of 58 point to 50 point there, 58.2, 58 0.2 stone. Yeah. I mean, is very important to get to use quite often in these problems. Hey, Stared. This is one of the longer ones because the list is so long not gonna have this long of a list. And if you have access to doing something with technology, like to be able to find this with technology and get your allows that that's 100% okay. But that's just how you show your work if you are required to. All right, so we're gonna subtract and square, so really go ahead and go through the list and do that. So 43 on a 58.2 gets me a negative. But remember, when you square negative, you get a positive. So you should get to 31 0.4 for that 1st 1 56 minus 58.2 squared gets us 4.84 You're OK. 78 minus 58.2 Squared 3 92.4 81 minus 58.2 Squared 5 19.84 47 minus 58.2 squared. Get this 1 25.44 40 to minus 58.2. Squared gets us to 62.44 and then ready for the next column. 34 minus 58.2. Squared gets us 5 85.64 20 to minus of the 8.2 on. Dsquared gets US 13. 10.44. It's a bigger number. All right, 78 minus 58.2. Gives us 19.8 squared. It's US 3 92.4 Okay, 98 minus 58.2 squared. It's this 15 84. That's a 12 0.4 All right. 38 minutes 58.2 squared. Get this. 408.4 46 minus 58.2. Gets a snake it of 12.2, but were squaring that we get a positive 1 48 0.84. Then 54 minus 58.2. Squared gets a 17.64 on this last call. Okay, 67 minus 58.2 is 8.8 and we square that 77.44 look a little nicer. 0.44 All right, 58 minus 58.2 squared. Get this point. 04 90 to minus 68.2 and then squared. Get this. 11. 42 point 11. 42 point for four. Your point for now. Okay. And then 55 minus 58.2 squared gets us 10.24 So after all that tedious work, I know that was a lot because our list was so big. Um, we're going to need to actually get the variation. So we get the variation by taking all three numbers in these columns, and we'll add them all up and find the average of that that was just the various. So it will take a little bit, but it will be fine. So we got to 31.4 plus four 0.84 plus 3 92.4 plus 5 19.84 plus 1 to 5.44 plus 262.44 plus 5 85.64 plus 13 10.44 plus 3 92.4 1584.4 plus 4 8.4 plus 1 48.84 plus 17.64 plus 77.44 plus 0.0 for plus 11. 42.44 This was before for and then last, but at least 10 0.24 We add all those up and we get a grand total of 7000 212.44 We divide by 17 and that will definitely to be rounded. It's 424.3. We take that 424.3 and we need to now use that to get the standard deviation so the sooner deviation is always a square root of the variants that we just got. So we're gonna square root the 4 24.3 and I think that look a little bit nicer. And then we get approximately 20.6 rounded to the nearest tense of make sure circle or square, your Final Two answers air the variance and the senior deviation as 20.6 for number five.

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