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Watch GTV, meaning that, 36% of Ghanaians watch GTV. This is an example of Descriptive statistics B. Population statistics C.Inferential statistics D. Sampled stati...

Question

Watch GTV, meaning that, 36% of Ghanaians watch GTV. This is an example of Descriptive statistics B. Population statistics C.Inferential statistics D. Sampled statisticsWhen researcher considers only part of a and any computed summary from that is known as A. population , sample survey, sample statistic_ B. population, population census, sample statistic C. sample, population census, population parameter D: sample, sample survey, population parameterhe conducts25Which of the following graphs is

watch GTV, meaning that, 36% of Ghanaians watch GTV. This is an example of Descriptive statistics B. Population statistics C.Inferential statistics D. Sampled statistics When researcher considers only part of a and any computed summary from that is known as A. population , sample survey, sample statistic_ B. population, population census, sample statistic C. sample, population census, population parameter D: sample, sample survey, population parameter he conducts 25 Which of the following graphs is most appropriate for quantitative data? Parcto B. Bar Chart C: Box Plot D. Pie chart 26. To convert relative frequency distribution to frequency distribution Find the difference between consecutive lower class limits_ Divide the class frequency by the total number of observations: C. Multiply the class relative frequency by the total number of observations. Multiply the class frequency by |00



Answers

Consider the following data. The summary statistics, histogram, and normal quantile plot were generated using Minitab. $$\begin{array}{lllllllllllllll}27 & 27 & 27 & 28 & 28 & 28 & 28 & 28 & 28 & 29 & 29 & 29 & 29 & 29 & 29 \\29 & 29 & 29 & 29 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\30 & 31 & 31 & 31 & 31 & 31 & 31 & 31 & 31 & 32 & 32 & 32 & 32 & 33 & 33 \\ 33 & 33 & 33 & 34 & 34 & & & & & & & & & &\end{array}$$ (a) Does the histogram indicate normality for the data distribution? Explain. (b) Does the normal quantile plot indicate normality for the data distribution? Explain. (c) Compute the interquartile range and check for outliers. (d) Compute Pearson's index. Does the index value indicate skewness? (e) Using parts (a), (b), (c), and (d), would you say the data are from a normal distribution?

Hello. Everyone in this video, we're going to use the five number summary and a box spot to look at. 10 ammonia flux is first things first to note we have 10 observations because it's even we know that we have to find the average of two numbers in this case will be the 5th and 6th position. So to find the average of these two numbers we do some quick math on the side. Mhm. 1 16 plus 1 47 is equal to 63 to 63/2 gives us 1 31.5. This represents our median. Okay please note because we made this 1 31.5, we should not include it in our countings when we're doing quartile one and cartel three. So next we only have five not including quarter to because we we made this um from our we made this um number from our averages. So we look for the eighth, the third position because there's five numbers. So quartile one is 88 on the other hand on the other side, the right hand side O. B. One 54. So let's mark this down. Oh three is 1 54. What's that? One 88. No to interpret these courthouse you can treat each section as a quarter similarly to a dollar. We have four quarters that's a dollar. So we treat each section um from 57 to quarter one, treat as 25 cents or 25% of our data. So forth as you move to the next section to the end. That's another 25%. Once you hit 43 you already 75% of the data. Next we'll move to part B. Which is inter quartile range quartile 31 54 minus quick out. 1 88 and that gives us 66. Yeah put this right there, 66 represents the range where we capture 50% of our data. If we were to look at quartile, one cartel three, we have two sections two quarters or 50% of the data. Part C Well look at the five number summary minimum 57 or top 1 88 without too 1 31.5. About 31 54 and a maximum 1 75. Next we'll look at party which is looking for outliers felt using or formula lower ground equal to do this over here. Lower bounds equal to 88 minus 1.5 times 66 which is our inter cartel range. And that should give us Yeah, negative 11. Upper bound we have 54 plus 1.5 times 66 she gives us 2 53. So if we have any observations below negative 11 will be considered an outlier. Any number above 2 53 would be considered another outlier. Because none of our observations are below nine of 11 or above to 53. We do not have any outliers and we can show that using our box spot. Please give me one moment to draw the box plot. Here's a box plot as you can see there are no outliers. Um so that means we were using our whiskers by using our five number summary. So I left most whisker 57 right Most whisker 1 75 red line represents quartile to left. Most first blue line represents quartile one right most second blue line represents quartile three.

Hello everyone in this video. We're going to use a five number summary, a box plot and portals to look at sunrise times. First things first to note. Make sure to organize and sort your numbers from lowest to highest and note the number of observations we have. In this case it's 12 because it's an even number. We have to find the average of the 6th and 7th position. So these two are middle numbers. So we actually have to find the average of these two numbers. Quick simple math. Because 3 64 oh sorry 3 96 is four away for 400. We'll meet somewhere in the middle let's say two away. So our median is doing 98. Okay. Okay. It's not because we made this observation we do not include it in our countings for quartile one or quartile three. Thus we have six observations on the left side. That means it's an even number. We also have to find another average the 3rd and 4th position. 3 54 and 3 74. Um Are are two numbers. Um Another quick easy math because 3 57 to 54 is 20 away from 3 74. Meet somewhere in the middle which is 10 away. The average is 3 64. Next you're fine, cartel three will do the same thing, 3rd and 4th position, but on the right side 1234 So we have 4 26 and 4 27 to meet somewhere in the middle. Well look at um how the distance between these two numbers which is one so half of one is 10.5. So we know that cartel three is 4 26.5. Mhm. Next to interpret these portals, the start of quartile one, we treat if you think of the word quartile as quarters uh in the sense of money. So four quarters we divided our observations into four different quarters. Starting with quarter one. All the observations leading up to 3 64 is 25% of our data to reach quarter to trita asked two quarters or 50% or 50 cent. All the observations from 373 49 up to 3 98 50%. Number data so forth with quarter quartile 3 75%. Number data. We treat each section as 25%. Next we'll move on to party inter quartile range which is okay. Four the 26.5 minus 3 64 which gives us 62.5 62.5 represents arrange where we are capturing 50% of our data. For example, between 3 64 and 4 26.5 we have two quarters or 50% of the data. Next we look forward to five. Number summary. Yeah. Our lowest or minimum number 30 49. Quick. How one 3, 64. Our quick how cute during 98 without 34 26.5 and our maximum 445 Make this a little bigger for party. Well look at lower and upper bounds. These two formulas will help us find high and low outliers. So starting with lower ground, we have found one big 64 minus 1.5 times 62.5. Yes, she gave us to 70.25. Upper Brown 4 to 6.5 plus 1.5 times 62 25. This should give us 5 20.25 His notes, we do not have any observations below to 70 or any observations above 5 20. That means we do not have any outliers. Now, let's show this. Using our box plot. Here's a box plot, as you can see. A box plot is very similar to our five number summary because we do not have any outliers are whiskers, the left most whisker and the right most whisker matches our minimum, and a maximum of five number summary. Red line represents our medium first blue line on the left side represents Corta one second blue line represents quarter to three.

In question. 136. You're now using the data sets provided by the textbook. So perhaps you have a CD? Probably not. Perhaps you have a link easily to find with that data. If not how I found it was You go to the supplements page in the digital textbook and on the bottom left side, you'll see this link to the Weiss website that has your data sets in it. Make sure you choose the right edition for the book that you're using, and then you're going to want to choose to download probably the text files. Um, is that's how I will be demonstrating it in this question. And, um, I had trouble downloading the text files and some web browsers. So do try different Web browsers and check under your downloads as you're trying to download those data sets from there. Okay, so just remember what we're looking for. We're going to do almost all of these steps kind of in one. You're allowed to use your choice of technology for these problems. I had difficulty figuring out how to use Excel, or he needs to find to create box plots with these data. sets. And I think that's just because the software changes over time and box plots are not tough on their priority of things to automatically provide. So we're going to use class couch, which is set up well for this type of activity. So you're gonna go to class Coke, and we're actually going to have to do a little bit of a work around because it's not perfectly set up. So we're going to begin by importing a table, even though a table isn't really what we want. We want to list. But this is the fastest way I found to use our data. So I've already got this set up. So it's going to my folder for this s nine text data, and I know that I want the data for question 1 36. So much hype that in there quickly open that data file, going to import it for me, and you can see it cuts out the middle part of the table. But it's there if you want to see it. It's just showing you that you have the 51 row table, and, um, again, I don't really want a table to use class cap to dinner. The blocks plot. I need a list. So what I'm gonna do is redefine my data as a list. Some type in a capital l one define that as the data found, an X one in the table above and you can see here when the bomb, right. It'll show me my data list there. So that's delightful. So I'm ready to go now. Now, I need my keyboard from down here, and I want to go under, stat. And I want to go under it, um, under plot, which is what I want. And I want a box plot and I want to tell it. Then I want to talk about using the data from l one. Okay. And, believe it or not, that box plot should be showing up on my screen. So you might ask yourself, Well, where is it? So you have to remember that it is charting using your data numbers, which are in the fifties, and it's using that on the x axis. Do you want to move your x axis over there, see how it's appearing in that fifties range? Okay. So you can make it bigger if you want this way, it's just running along. Why goes one? The important thing is that the X values are right there in the fifties. So there's my box plot. If you need a little. If you want the list of the portals, you can click that bottom right button there and we'll give you the exact portals. So from here we can get most of what they're asking us for. Let's go back and check our list. We want the court ALS. Okay, so that's there, Child One. Remember that the median is caught up to three in the max. Escort out four and it also wants to intercourse to arrange to remember. That's the difference between the 3rd and 1st quarter house. So that's the value of three. So 56 months 53 gives me three. It also wants what it calls the five number summary. Well, that's those five boxes you see right there the min Max and the Four Tops. And then it wants a box plot. But you have a picture for here. And the final thing is, it does want to check for any outliers. Okay, so just in case our feature didn't do that correctly, you're going to want to take the first quartile and subtract 1.5 times the inter quartile range. All right, so that means that my lower boundary to be at 48.5. So that's interesting, because it does show a minimum value at 48 which technically does lie below my boundary. So that 40 those 48 values technically are outliers. So, um, we may want to go and delete them to correct our box plots while we're before we do that. Let's go double check at the upper end. So that would be we take our third quartile. We add to it 1.5 times inter quartile range and, like there's a 60.5. Okay, so that's definitely way over here. There's no data above. Do you have these two data points that seem to fall below? Assuming that this data is in order, it's just kind of double check that again. Yes, They have ordered this data set for us, which is very nice. So I think what you want to do is actually go in here. And if we don't think you can edit in here, But I think we can edit it up in our table and let's go in and actually try to delete those first two values in order to correct our boxes. Lot, make it better. So I rushed to go with police those numbers, and we're gonna regenerate this definition that regenerates us. 49 items on the list. Still says 51 but notice it could adjust my values. Okay, so it did take those data. Points out, um, an O. Look, there's a button on here. We could have just excuse. Let's put it back. Let's put our 48 back and just choose this point down here that says exclude the outliers. Interesting. So it tells me that there's two items there, but interestingly, it did not adapt the box plot. The courthouse. It did not change the box, so I like it better. Um, go ahead and delete those to get what your boss boss should look like. Okay, because you're more accurate. Box plot there. Okay, so I think that's better, right? I think that, um, answers other than they asked for interpretations. Prime. Clear. If you're writing up your answers, um, you're going to have to say things like, um, for chortled to say, 25% of the data, um, falls below that 53 was my first quote job, but they may even want more specific to the story, which was about the percent of women attending colleges. So you could say, and 25% of the states, um, 53 percent or 1/4 of the state's 53% or fewer women attend college in. So for them, for the median or the second court valued, say, let's check our data. You say there's our medium is 55. So I would say in half of the states and D. C. 55% or fewer. Um, yeah, 55 or fewer percent of students attending college are women. CNN is first of all in all of the states, right? The minimum is 50. That means in in every state in the nation, at least half of alcohol students are women and mostly more. Right. Um, so in 75% of the nation, that number is up to 56% or your nights looking around the, um so anyway, interpret them as you will that way. So, um, the I Q R and an interpretation of it. You've got to say like, um, the middle 50% of states have between 53 56% of their college students are women. And, um, similar comments for the five number summary and the outliers. Okay, so you can say the two states where where there were fewer than 50% of college students who are women were considered outliers. So okay, so that's a lot of interesting discussion for you to ride up, and that's all for today.

Yeah. Question 1 36 gives us data. Uh, for the 50 states and the District of Columbia, which gives you a total of 51 data points and the values in the state is set represent the percentage of college students that are female was very interesting. So the first challenge in these problems is to access your data. If for some reason you don't have a CD provider or you don't have a CD player to use that CD. So I've given the instructions down here. Find the page label supplements, either in the digital or the heart condition. Follow the link in the bottom left part of the page for the Weiss Web page, choose the correct edition of your book and then download either the text file version or the Excel file version for this question because it's a simple set of data provided we can just use the text version of the file. So we're going to go put that in the class couch software as far as to answer kind of all of our questions all at once, you know? So they've asked us five distinct things here, but we're gonna execute them all at once. So we're gonna go over here and begin by importing our data. And the only option in classical right now is to import it as a table. So we'll do that. This is question 1 36. So there's our data. You'll notice our numbers are in the fifties and such, so that will become applicable in a minute. But that makes sense. Percent of college students as females. The next thing we need to do is convert this table to a list format, which is really what we need to do box pots with for simply redefining. I simply typed in l one equals x one. It automatically reformatted at those s sub scripts for me. And then I can simply tell it that I want to do a box. But notice a fiber correctly expects that, and I tell it which list I want to use for the box plot. And my window is already already sized. Okay, if for some reason your window isn't showing the box plot here, the reason is you just need to slide or go up here where it says graphic in the top right corner. Where has that radiant thing and set your X Men X max. You know your lower and upper bounds for your axes to get a good picture. So my I've got touch screen though. So Well, just future over there. Okay, so there's our picture, and then we want before we're confident that this is our box plot. We do want to check for any outliers to exclude. So we're gonna click on that back in there. And this is this particular data set. The software behaves a little bit interesting in that it does put a nice X on the outlier, but it's not adjusting the box block as it does for other days. It's for some reason. So we're going to actually go in and delete those because 48 is an outlier or to get a nice box by works again. Look at that off. It actually only made me cut one of them off to adjust the box pot correctly there because 48 does lie just barely outside the range. So just a reminder of how you calculate whether something is an outlier. You do want to carry that 1.5 pines interpreter reigns with those 56 minus 53 the 4.5 above and below my 1st and 3rd quartile. So if I take my first quartile of 53 minus 4.5 puts me down at, like, 48.5. So that's really close there to that minimum that those 48 values we had. But technically, I think you should cut them off and adjust your, um, just a box plot accordingly at the upper end. If we took 23 and added 4.5 would get up to 60.5 and our maximum value is 80 so we have no outliers at the upper end there. So that's your picture that answers you can pull from here. Your portal's Remember the meeting is your second quartile and your five number summary. You can see in the gray on the left and your box plot values. So the only thing left to do is the interpretations of these. And so this could be an extensive lots of sentences that you could give for an answer on this. A judge from your teacher, how extensive you need to answer this, but certainly gives some interpretive sentences such As you know, the middle 50% of states have between 53 56% of all their college students are female, or you can make a lot of interesting comments like, um, the only states they were the only, you know, states or districts surveyed in which females are a minority. In other words, less than 50% are considered outliers, statistically only in two states. So or you could say something like, um, the state with the highest percentage of college students as females has 58% of its college students are females. So, um, so you can make right a variety of interpretive statements describing, um, the implications of these courthouse and data plots. That's all for question 1 36.


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