give-a-sample-set-of-data-with-a-variance-and-standard-deviation-of-0

Name: give a sample set of data with a variance and standard deviation of 0
Uploaded: 2020-06-03
Duration: 2 min 1 s
Channel: Numerade
Description: Give a sample set of data with a variance and standard deviation of 0.

Question

Give a sample set of data with a variance and standard deviation of 0.

Trinity Steen · Accepted Answer

Okay, So for number 34 this is one of those answers May very kind of things in there several different ways. You can go about this and choose this, and it&#x27;s actually pretty straightforward. So you&#x27;re trying to figure out a Senate aviation variants that both equal zero. So if you&#x27;re variants equals zero, the square root of zero is zero. So our main focus is going to be trying to be able to figure out how to work backwards and get a variance that&#x27;s gonna lead to a zero. And it&#x27;s actually pretty straightforward. So I&#x27;m going to do one example. But once you use that you see my table, you can come up with your own relatively straightforward. So basically, you would need to have a list of the same numbers. That is one way you can go about this. So what I mean by that is say, I want a list of lives. Well, here&#x27;s how that would work. If I get a list of five, I need a have five of those in my list because what will then end up happening is if I go and I get my bar, I dio ah five plus five plus five plus five is 25 divided five. You know it&#x27;s five. We&#x27;ll hear a call from previous problems to get your variants. You take all the numbers in your list and you&#x27;re subtracting them. So five minus the mean is going to get me zero. And that&#x27;s what zero squared is still zero. So we&#x27;ve made our goal. So this would also have worked because if I keep going and keep going, I&#x27;m gonna get 0.0 and we all know that still zero, So that is going to be awesome. So if I did a list of four force that could work as well. And so basically, you just do however many numbers of whatever number you pick, so you pick 10 you&#x27;d have 10 tens in your list, and that will still get you your Senate deviation and variation, both being equal to zero

Deborah Ferry · Answer

we will begin by entering our six data points from the sample. And then again, we can asked the calculator to calculate variance for a sample. And her data is in the column. We named data, so it&#x27;s 877.38 and the standard deviation or again, our sample in the data column is 29.6.

Karen Song · Answer

here were asked for the mean. Our just assumed that the question is asking for the population. So, um what? Just trying to ask Mu. You issue call two more hours he&#x27;s found. The question says It says approximate bite to occur for hours each to do the review. Our here we have the mean and what&#x27;s the standard deviation euro We use seeking lets you denote this value. And in this question, it&#x27;s equal to one point to you our as Cuban in the question and the sample size symbols, I you really used small pin to note that the simple size and in this question in 16 we can&#x27;t.

Derrick Hanson · Answer

we&#x27;re being asked here to find the variance and the standard deviation for this set of values. Uh, first thing we need to do before we can even begin finding variants or standard deviation is we have to find them mean meaning the average. So we need to take all of these numbers and add them. 12 plus 14 plus 28 plus 19 plus 11 plus seven plus 10. You need to add it all. Okay, If we do that, we get 101 and then we need to divide that by how many data values we had. Just 1234567 So we&#x27;re taking 100 and one divided by seven. That gives us 14 0.4. This is are mean. Okay, now, now that we have our mean, we can actually start trying to find the variance. So find our variance. What we&#x27;re gonna do is we&#x27;re going to take our data value each and every data value, and we&#x27;re going to subtract that by the mean. Then we&#x27;ll square whatever we get for each number. Meaning I&#x27;m gonna take 12 minus 14.4. I&#x27;m going to take 14 minus 14.4. I&#x27;m gonna take 28 minus 14.4. I&#x27;m gonna take 19 minus 14.4. Gonna take 11 minus 14.4. Thank you guys there. Hopefully getting the idea here. I&#x27;m gonna take seven minus 14.4. And I&#x27;m also gonna take 10 minus 14.4. Every single one of my seven data values from the beginning of the problem are gonna be subtracted by the mean. And then I will square what I get from them. Okay? So 12 minus 14.4 is negative. 2.4 when we square that we would get a positive 5.76 Remember that any negative number squared does become positive. If you&#x27;re not getting that in your calculator, you need to use the parentheses like I&#x27;m writing here. You have to use princes. 14 minus 14.4 is negative. 0.4 when you square that you would get 0.16 Not a big number, but it is still positive. 28 minus 14.4 is 13.6. When you square that you get 184.96 it&#x27;s a lot. 19 minus 14.4 is 4.6, which Squared gives US 21.16 11 minus 14.4 is negative. 3.4. When you square negative 3.4, you would get 11 0.56 seven minus 14.4 is Ah, negative 7.4. And when you square that you would get 54.76 10 months, 14.4 is negative. 4.4. Which one squared? We&#x27;ll give you 19.36 That was a lot of math. And don&#x27;t worry. If I&#x27;m doing that faster and you can put a plug in your calculator, you can always pause the video and do that stuff to check to make sure you&#x27;re good with everything. Okay? No, basically, what we have to do to find variance is we have to take all of these new numbers that we just found, and we need to find a new mean and on average, from those meaning. I want to add up all seven of these new numbers and divide them by seven, because that&#x27;s how many data values there are. So if you take all seven of these numbers, all of these numbers right here. These numbers are what we&#x27;re talking about. If you had all of those up, what you should get is 200 and 97.72 That&#x27;s what you should end up with here. Then we have to take that and divide it by seven. Because we had 1234567 Data points. 292.72 divided by seven is 42.53 That is your variance. It is not the end of the problem, though, because we were also asked to find the standard deviation. Standard deviation is simply just the square root of the variance. Okay, so if you want to find the standard deviation, you simply just need to take the square root of 42 0.53 The square root of 42.53 is equal to about 6.52 And that is the end of your problem because you have found both variants and standard deviation

Derrick Hanson · Answer

All right. So we have been given this set of numbers and ah, we have been asked to find the variance and the standard deviation. Okay, this is a bit of a process, so focus in, and this may be a little bit longer than some of the other questions have taken. All right, the first thing we need to do to be able to figure out the variance and standard deviation is we&#x27;re gonna need to calculate the mean for this data set. If you don&#x27;t have the mean you can&#x27;t find the variants of standard deviation came over mean is the same thing is average. So what we&#x27;re doing is we&#x27;re just going to add all of these numbers up seven plus 16 plus nine plus four plus 12 plus three plus nine plus four. All right, And then we&#x27;re going to divide whatever that total is by how many numbers we added together. Meaning, since there are eight numbers in this data set organ divide by eight. Okay. If you add all those numbers up seven plus 16 plus nine plus four plus 12 plus three plus nine plus four. You get 64 64 then gets divided by eight, which gives us eight. The vat is are mean. We have a mean of eight cane. So that&#x27;s useful knowledge. We want to keep track of that. All right, now that we know are mean is eight. We can actually go about trying to find the variance. Finding the variance is a long well, maybe not super long, but it is. It is a a series of steps. The first thing we&#x27;re gonna do is we&#x27;re gonna take every single one of these data values. Meaning seven, 16 94 12 39 and four. And we&#x27;re going to subtract all of those by the mean meaning we&#x27;re doing. Seven minus 8 16 minus 89 minus eight four minus 8 12 minus eight three minus 89 Minus eight and four minus state. Okay, we&#x27;re taking the data values minus the mean. I can&#x27;t even write that here. Data value minus mean. That&#x27;s what we&#x27;re doing here. Okay? After we do that, we are also going to square each of those parts. So seven minus eight is negative. One negative. One squared is positive. One 16 minus eight is eight. Eight squared is 64 nine minus eight is one one squared is one four minus eight is negative for negative. Four squared is 16 to remember that any negative numbers squared becomes positive If you&#x27;re plugging this into your calculator and it&#x27;s giving, you know, gave numbers after you square, you need to use the parentheses the way I&#x27;m writing them here. 12 minus eight is four for Squared is 16. The same thing is negative. Four squared three minus eight is negative. Five negative. Five squared is 25 nine minus eight is one one squared is one that one kind of got off track. Here we go. Four minus eight is negative. Four. Just like it was above negative four squared is 16. All right, so we have taken every date of value minus the mean and then squared it. We squared us that they&#x27;d all be positive right now, what we&#x27;re gonna do is we&#x27;re basically going to calculate another mean meaning. We want to take all these numbers that we just found, and I want to add all of those up and then divide by how many there were meaning. If I add all of these numbers up one plus 64 plus one plus 16 plus 16 plus 25 plus one plus 16. I get 140. Okay, so now I&#x27;m going to take that 140 and I&#x27;m going to divide it by how many data values I added up, which is 12345678 So I&#x27;m taking 100 and 40 divided by eight. 1 40 divided by eight gives me 17.5. This is my variance long process. Like I said, you have to find the mean yourself first. Then you take each of the data values that the book gave you and subtract it from the mean or subtract the mean from it square to get everything positive. And then you get to find the mean again of all those new numbers that you just found. We&#x27;re not even done yet because we do have one more step because it also asks us to find the standard deviation. If we are asked to find the standard deviation. Standard deviation is simply just the square root of the variance. That&#x27;s all. Standard deviation is okay, So standard deviation is the square of the variance. Then that means all I have to do is take the square root of 17.5. The square root of 17.5 is roughly 4.2. That is our standard deviation.

Deborah Ferry · Answer

we begin by entering the data into a list in spreadsheet notice. We have all 10 of our items, and then we can ask the calculator. We can say equal variance a sample and identify the column. We called it data and we get 648 point 99 roughly. We can also ask for the standard deviation of the sample, and we need our data, which is in the column called Beta, and we get 25 point for eight, roughly.

Problem

Find a counterexample for the following statement…

Problem 34 Hard Difficulty

Give a sample set of data with a variance and standard deviation of 0.

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