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1) Given the following sample data: 18 21 32 41 Calculate the sample variance. Keep to 2 decimal places.2)Given the following sample data: 18 21 32 41 Determin...

Question

1) Given the following sample data: 18 21 32 41 Calculate the sample variance. Keep to 2 decimal places.2)Given the following sample data: 18 21 32 41 Determine the sample standard deviation. Keep to twodecimal places.3)The hourly wages of a sample of 130 system analysts are givenbelow.MeanMedianModeRangeVarianceStandard deviation6074732032418The coefficient of variation equals.a) Given the mean is 13, the median is 10 and the standarddeviation is 4. Determine the coefficient of skewness. K

1) Given the following sample data: 18 21 32 41 Calculate the sample variance. Keep to 2 decimal places. 2)Given the following sample data: 18 21 32 41 Determine the sample standard deviation. Keep to two decimal places. 3) The hourly wages of a sample of 130 system analysts are given below. Mean Median Mode Range Variance Standard deviation 60 74 73 20 324 18 The coefficient of variation equals. a) Given the mean is 13, the median is 10 and the standard deviation is 4. Determine the coefficient of skewness. Keep to 2 decimal places. Do not convert to percent.



Answers

Sample annual salaries (in thousands of dollars) for employees at a company are listed. $\begin{array}{lllllll}42 & 36 & 48 & 51 & 39 & 39 & 42 \\ 36 & 48 & 33 & 39 & 42 & 45\end{array}$ (a) Find the sample mean and the sample standard deviation. (b) Each employee in the sample receives a $5 \%$ raise. Find the sample mean and the sample standard deviation for the revised data set. (c) To calculate the monthly salary, divide each original salary by $12 .$ Find the sample mean and the sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?

That will always be your first steps. So you look at your list and you count how much you have in your lists. It turns out there's nine. So remember the mean or the average is the same as adding up all of your numbers in your list and then dividing by night. So we're gonna add up the 2.4 plus the 5.6 plus the one 0.9 plus the 7.1 plus the 4.3 plus the 2.7 and 4.6 and the 1.8 and the 2.4 and you get 32.8 already. And then you divide that by nine, and you get 3.6 officially rounds to the nearest 10th of 3.6. So you're going to be using a 3.6 quite often in step two. So very of the seeing how far away your spread is from the mean So, um, we're going to take all the numbers in the list all not above, and subtract the six, the 3.6. So I'm gonna write 2.4, minus 3.6 and 5.613 point six and noticed were squaring because when you subtract, sometimes you're going to end up with negatives. But we can't have negatives were doing very interesting a deviation. So we square that remember whenever you square negative, it becomes positive. So that's why the squaring is going to happen eventually. Sort of subtract first, then square for all nine of these items in the list. So 2.4 minus 3.6 and then we square it get 1.44 Okay, 5.6 minus 3.6. And then I spirit we four. Okay, 1.99 of 3.6 and square it. We get 2.89 7.1. Line 3.6 and square it. You get 12.25 4.3 minus 3.6. Squared is 0.49 2.793 point six squared is pointing one 4.6. Lie in the 3.6 is one. So once weird is one as well. Uh, 1.8 my nephew 0.6. It's negative. 1.8 weeks for that 3.24 and then 2.4 minus 3.6 square is the new one point for four. So the variance officially is the average of all of these numbers that we just calculated. So that means I'm gonna take all nine of these numbers and find the average of so we Adam and divide by nine to get and that will be our variants. So 1.44 plus four was 2.89 plus 12.25 plus point for nine plus 90.81 last one plus 3.24 plus 1.44 Get us 27. 56. Do not turn out nicely. Much weather. Okay. And then we divide that by nine. Okay, so we get 3.1 when we round to the nearest 10th which is what you're gonna probably need to do on some of these. So 3.1 is one of our final answers. But then we take that 3.1, and we use that to get the sinner deviation as our finals at the standard deviation is very simple. You just take the square root of the number that we just got that 3.1 and you scared that and around the near sent, and you should get approximately 1.7. Now, if you square root the whole thing that's from your calculator. It is 1.7. But if you just do the square root of 3.1, then that around a 1.8. So it just depends what you put in your calculator. So I would say, based on the fact that if we're rounding to the nearest 10th here and then we input that into our sin deviation, that's more likely going to work out of your final answer number. Sure, you're a teacher, revealing it with that. It just depends on what they're rounding. Specifications are, so make sure you ask your specific teacher.

We begin by entering the data into a lists and spread sheet page in the T. I inspire handheld notice that we've entered all 12 data items and then we can go to a calculator page and asked for the variance of the population again. We called it just data, and we can also ask for the standard deviation of the population for the data set, and that will give us 10.8.

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.

Oh, right. So, four, these particular problems that are asking you to calculate the variance or and this dinner deviation given a certain list of ida of numbers, um, my best rubber. My best recommendation would be for you to go to Dez most dot com. And then you just click start graphing anyone actually to grab anything. But this works as a graphing calculator over here. So Step two, you're gonna find variants by typing V a r p so that p stands for population. That means you're given the entire list. Ah, that exists. Ah, for the particular information. And you're going to wanna have that p there instead of not having that, Peter, because you'll get two different numbers otherwise, and then you're ready to enter in your list of your number. Sore list of numbers is 48 comma. Make sure you're comin out a decimal. 36 40 29 45 51 38 47 39 and 37. So if you see here, answer. They're gonna be displayed in the lower right corner right here. So it's exactly 40. So there's no rounding necessary. And then to find the standard deviation. You're gonna type S T D E v and then api again for population cause you're given the entire list. You're given the entire population of information that exists. So we're gonna cut, copy and paste your list so you don't have to re type it all up again. So 6.3 right of the nearest 10th is going to be your sooner deviation for this. Now, another way you could get us in a deviation is if you look at your variants value and you square root it so you would dio square sq rt for root, and then your simple shows up 40 and you'll notice that they're the exact same.


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