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Find the mean and the standard deviation. USC correct symbolsThe mean:The standard deviation:kCreating a Set of' Samples We select samples of size two with rep...

Question

Find the mean and the standard deviation. USC correct symbolsThe mean:The standard deviation:kCreating a Set of' Samples We select samples of size two with replacement:How many samples will we have? (hint: there are 8 choices for the first value and then 8 more choices for the second value) List all of the samples of size two with replacement: Next to each pair include the meanblt

Find the mean and the standard deviation. USC correct symbols The mean: The standard deviation: kCreating a Set of' Samples We select samples of size two with replacement: How many samples will we have? (hint: there are 8 choices for the first value and then 8 more choices for the second value) List all of the samples of size two with replacement: Next to each pair include the mean blt



Answers

Find the mean and the standard deviation for each set of values.
$$
6 \quad 1 \quad 9 \quad 12 \quad 4 \quad 15 \quad 21 \quad 7 \quad 8 \quad 8
$$

When tackling this problem, hopefully have some software at hand whether it's ah, graphing calculator or software online. But really, all you need to do is input these data values into your software. It will calculate the main and standard deviation for you. So in this case, I found a standard deviation calculator online, and I'm going to go ahead and input all of these pieces of data in 89 may push calculating and will give me all the information I need. So the standard deviation between just called SD or you can call it, um, the Scripps Simple Omega. It's 5.6 and then you look around, you see this symbol here, This is mu or in math, that means Mean mu is kind of a fun simple to try to rate of 7.7 and you are all done

This question to ask you to calculate the mean and standard deviation. Um, I could show you how to do this by hand, but I used a calculator, and I think most, um, most math classes. You should start to get comfortable with using the technology you have to calculate mean and standard deviation. The mean is found by adding all of visa. So if you take 12 plus 13 plus 15 post nine post 16 plus five was 18 post 16 plus 12 plus 11 plus 15 you get 100 and 42 and then if you take that sum of 142 and you divide by the number of terms, which is 11 that's the average, which we often use the notation of X bar for average. That's about 12.9. And this is why, ah, having a calculator do this calculation for you? Ah, in a robust programming type calculator, like a graphing calculator, you're not gonna have to do all of these simple calculations. So the standard deviation is felled by taking each data value X and subtracting that X bar, and then you want to take all of those differences and you wanna add them up, so that's a notation of signal of adding them up. But if you add all of them up, you're gonna get zero. So before you add them, we actually square them. This makes all the numbers positive. It gives numbers that are close to the mean less weight. It gives numbers that are far from the beam or way. And then this is where it gets weird. We want to divide that by N by this What? That gives you the standard deviation. All right. And the best explanation I've heard for why buy this one? It's because you're kind of including the average in the average really isn't in there. So we're taking that average out. Um, to be honest, I don't love that. Ah, that reasoning. But I think you need a PhD and stands to really explain to me why it's a minus. What? I just know it works. So I take 12 by this point night and I get negative Point night. I take 13 by his 12.9. I get point would 15 by this 12 point night, and I get to point what died by this 12 boy died, right? I don't know what that is. Up top my head! Aah! Because a three point die, they get three Point Guy 16 right? Is 12 point. That was at 3.1 five by this 12 point I. What is that? 7.9, right. These numbers are not fun. So there you have. Take all those numbers and square pointing square. That's 0.8. What point would square? That's point. Oh, right. Do boy would squared. I should be able to do that in my head. But a four point for what? I do That so then I have to add all of those squares up. Right? So this do Raiders often called the sum of the squares. And when you do that, you're going to get about 37.0 would to to write that goes up. And so, you know, getting that the standard deviation is about 3.7. I found this with technology, and I highly recommend that you do the same

Yeah, The expectation allow ads equals the integral of ads times it's probability density function. So this is from 0 to 2. Eric Starnes 3/8 X squared dx. And this echoes 3/2 the expectation of X squared is integral of X squared times probability density function. These vehicles the integral from 0 to 2 X squared times spray over eight X squared dx, Which he calls 12 4 or five. So the bombers echoes the expectation of X squared miners. The square of the expectation relax. Did you get your coals? 12/5 miners? Three half square. Which vehicles 3/20? The standard division And just as the square root of the variance Pacheco's The square root out 15/10?

When this question, we're told that we have a random Sample size of 2 25 drawn from a population, The population has mean 100 and standard deviation 20, and were asked to compute the mean and standard deviation of the sample means, so the mean of the sample mean is just the population mean, which is 100. The standard deviation of the sample mean is the standard deviation of the Population mean, divided by the square root of N, which is 20 Over 15, which is square out of, then that's 1.33.


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