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1. (40 pts) Find graph on the intemet Or in newspaper, scientific journal, Or magazine that shows Gonc data_ Be sure print; clip_ or copy the graph and include it w...

Question

1. (40 pts) Find graph on the intemet Or in newspaper, scientific journal, Or magazine that shows Gonc data_ Be sure print; clip_ or copy the graph and include it with your assignment; ease say Where you found the graph_ Write short, coherent paragraph about the graph_ Be sure t0 address each of thesc four issues: Summarize what the graph says that is, the story it tells about the data it shows Wnat point is the person who made graph trying to convince the viewer of? What data are depicted? Are

1. (40 pts) Find graph on the intemet Or in newspaper, scientific journal, Or magazine that shows Gonc data_ Be sure print; clip_ or copy the graph and include it with your assignment; ease say Where you found the graph_ Write short, coherent paragraph about the graph_ Be sure t0 address each of thesc four issues: Summarize what the graph says that is, the story it tells about the data it shows Wnat point is the person who made graph trying to convince the viewer of? What data are depicted? Are yOu convinced by the graph? Why or why not? Critique the graph using the prineiples and terminology of Tufte (specifically: showing the data accurately and honestly minimizing data-ink, and avoiding chartjunk). What is good about the gruph? What is not good about it? Be specificlll If you think the graph could be improved, redraw it in detail by hand (Or On the computer) and explain why your versio better than the original, If the graph is perfect (not many are!) , give detailed explanation of why it is perfect:



Answers

The following graphs illustrate the incidence of pertussis (whooping cough) cases in the United States. The first graph organizes the data by year from 1922 to $2012,$ with the inset showing a zoomed-in view of $1990-2012$. The second graph organizes the data by age group from 1990 to 2012 . (The 2013 data are not complete in either graph.] DTP. Tdap, and DTaP are different formulations of the vaccine that covers tetanus, diphtheria, and pertussis. a. Describe what the first graph shows. What do each of the axes represent? What does any point on the line show? What general trend is seen, if all the data shown in the graph are considered? b. Why do you think there was an increase in cases of pertussis in the first decade of the twenty-first century? c. Describe what the second graph shows. What do each of the axes represent? What does any point on each of the different lines show? What general trend is seen, if all the lines are considered? What differs among the lines? d. Compare the incidence of pertussis cases in children under 1 year old and people over the age of 20 . e. Summarize your reflections on reviewing these graphs and the relative risks of pertussis and the pertussis vaccine. What would you recommend to someone trying to decide whether to vaccinate a child?

So this question says that if firm has a fixed cost for $60 and the total cost is on the variable cause as indicated in table at the top of the next page, I'll be joined a table. So were asked to complete the table on check out calculations by referring to problem for at the end of Chapter 10. So the first question was just to grab the total fixed cost the total fixed cost total variable cost on total cost. On explaining how the law off diminishing returns influences the shapes off the variable costs on a total cost coughs. So I'm gonna be doing that first. So so traffics crossed the 60 right andi to the Our cost is calculated by total cost is calculated by summing the total fixed cost plus total variable cost, so total cost is total. Fixed costs was total. Variable costs and average fixed costs is equal to total fixed costs divided by total products average. It's our product. I'm sorry about this. So average variable cost is equal to total variable cost divided by two top productive on average total cost because to total cost divided by so tell product imagine how costs equal to total cost and unit minus total cost and matters want unit divided by one. So now we're going to draw the table now that we have all the formalized. So we're going to start with to top product here. Right then. Okay. Now we have to top product fixed costs we have Very because we have to tell cost. We have outreached fixed cost. You have average way because we are average total cost. I only have. Imagine off course. Then we feel the total products we want to 10 zero wants to three or bye. 678 My to never drove the table. Don't. So from there we can solve it. So we have all the formulas, so that makes it easy to find to solve it. We had a total fixed cost already. So, general feeling the table on the fixed cost is 60. So we just feel that in. So because of the formulas, we have it easy to, you know, find everything else on. This is out. This is the finishing of the table. Once you have the form, lads, honestly, easy to find the rest. So now we're going to be joined the glass because the question also wants us to graph the what we just followed out. So, yeah, we're gonna join the graph. So this is our cost. That's the old spuds. Andi, we have fifth C on dread up to 500. Right? So this is the total fixed cost on this. The output over here and this is going to be one to turn, wants to to 10. We will. 56789 10. And then this is 100 to 500. So we're going to be having a point at one on. Could be having a point here. We're gonna be having a point on one at 50 hipsters right here. So one of 50 would be having a point at the total fixed costs on this right here. Going to be having a point to and almost 100 right here. Could we have any points at 102 right here. We're gonna be having the 0.3 on. So, basically, that's how the light should go. One would be we're gonna be using the green line to draw a green to draw this one. So she looked like this and go this. And then God said this. I'm gonna go like this and then three on almost I want 15. You should go like this, then, for, um, almost ad 4 50. She go like this than five on almost that 200. So did you connect than six ads? Most That's 200 then seven arts almost adds 300 eight ads. Almost that for 3. 50. Then we have night almost at 400 10. Almost adds 4 50. So this is how this line should connect on distributed total variable cost right? And then the second life would be the sea to tell cost for the total cost. It should be something like this. You should follow you right at both. And be something like this in coma, right? Like this. So this is a village hotel. Of course you'd better if you're joining on the people that way to be, you know easier. But this is what the graph should look like on this shows graphically the fixed costs. As you can see the variable cost on the total cost data. The total variable costs T V c is measured practical e as you can see votes valley on the front from the original access at age output on the fixed costs. CFCs are dead verticality to the total variable cost cough to obtain the points on the total cost. Cough C. C. So we can see that CBC on T c calls photo on Oprah trained. The justices are portrayed from 0 to 4 range of outputs, and this is because the cops slopes downward at the decreasing rates because of increasing marginal returns on the slopes. Increase at an increasing rate at the machining as the amenity imaginable rates or call. So that's that. So we can say that the coughs slope upwards as a decreasing rates us increasing imagina returns or call ah slopes downward. Mhm. So this is what it should be. The answer to the question extent how the law of the mission return influences the shape off the variable costs on hotel cost cost. Now, the next question it says, graph the average fixed cost average to tell, very because average total cost. I imagine it'll cost explained. The divisional shapes off each of the cubs on the relationships one another on explaining explain why I m c carvings of sex both the every season and the 80 psi Cops are their minimum points. So I'm going to start by joining the graph that shows the emcee every total cost. I read Saddam cost on average variable costs clubs so you might take a while. But let's draw it together. So this is the outputs on This is the cost. So I'm going to draw from zero to so one thing. So we should have this. I want to tell him so the average cost should be diminishing from 61 all the way to five on 10. And she looked like this. This is the average total cost. Now the average variable cause you look like this from one and four c. So and should go all the way to 10 on 50. And you look, you should look like this. Average variable cost. Now, the next one which is the average of the culture, look like this from here all the way down to 10. 60 100 stand a 60. So she looked like this. And this is average so that our cost and now the next one which is the Imagine All costs should look like this, So yeah, she looked like this. So this is what it calls you look like. And this is a marginal cost. So you're rushing something similar to this Andi, That's that's so the average fixed cost. As you can see average trees cost called false continuously. Since a fixed amount of capital courses spread over on the imaginable cost the average variable cost on the average total cost clubs I use shaped as you can see and reflects increase off first increasing and the Indian issue with tones. So we can write that on the average hotel costs, which is this off sums Average fit cost on average. Very because Brexit Carly So this and this is a call to this now the average total cost false when the marginal cost cough is below it. The average total cost curve rises when the marginal cost cough is above it. So average total cost, called false way, is below it. On average, total cost called rises when marginal cost is Abovitz. Now this means that imagine how cost cough wasn't just set. The average it'll cost on the average review cost cough answers minimum point so marginal cost on average variable cost, and that's that. So the last question the last question is explain how the minimum no explain how the location off each cough craft in question to be would be altered if one so tell fixed costs as being $100. So so tell. Fixed cost. I'd be $100 rather than 60 on variable to talk variable costs. So it's all very because I've been $10 less at each outputs, you know, I'm less of that. So if to tell very because I've intended last letter at each level outward imagine our costs would have been sent dollars lower, too, for the first units of outputs will remain the same for the main outputs. So marginal costs would have bean $10 Noah or the first units, right? What you made the same after. So the average variable cost on average total cost closed would also be lower by amount equal to $10 divided by specific output. So average variable cost on average with our cost cause would have been lower by $10 provided by the out foods. Right. So as a fixed costs are fixed, fixed costs are fixed obviously on did you not depend on variable? Cause on the average fixed costs will not be affected by the change by the change in Very because so average weeks closed called won't be affected by change because fixed costs are fixed. So yeah. So now we'll be joined the graph to show that so she looks like this zero. So 46 8, 10. Thanks, wolf. Right. And this is the hotel products, By the way, this is the cost on it. 0 200. Okay, then we moved to this. So this is average fixed cost? Yes. So we don't get confused. The red one is average. Grable costs the green. One is average. Total coast on the black form is marginal coast. So what wants to be drawing each line? So the blue one, you should look like this. Why? I go all the way to stand like this. So she looked like that. Then the next one, she looked like this. Then them black one, which is imaginable closed. So she looked like this. So this already, this is what the grass you look like on That's the numbers. Average rates, cost average variable cost, um, average, total cost and marginal cost. And that's it

We are given a sample of data points X. Y. Listen to the top of this white board and we want to use this data to answer the questions A through F. As follows. And part A. On the left. We want to draw a scatter plot for these data points. I've already included a scatter plot and the data points X. Y. Are demarcated with the black crosses or exes Next in part B of the right. We want to compute the relevant some of this data as well as the Pearson correlation coefficient. R. I've already included the value of the sums as they are simply found by following these equations exactly. So some acts of some of the X values, some wise some of the Y values and so on. Next you complete. You are using the following formula which takes as input the sum to just computed as well as the sample size. And Plugged in gives r equals negative .973. Next for part C. Let's find the line of best fit. First. We have to find the X and Y means X by Y. Bar found by dividing by N. The sums for X and Y. Next we find the slope and intercept for the best fit line. Be. The slope is given by the formula here it takes its input N. And the sums computed above. So it's very similar to the correlation coefficient. R Plugging in to get equals negative .11 And plugging in b. x. bar and wine bar to a give us our intercept three producing line of best fit. Why Pat equals three minus 30.11 X. Next you were trying to scatter plot to plot. Ry hat we make sure to mark our ex me and what I mean, producing this. Next we go to the bottom right. For part E. We want to calculate the correlation coefficient or rather a court coefficient of determination. R squared, which is the square of the correlation coefficient and interpret its meaning. R Squared is simply .946. We interpret this to mean that 94.6 of variation in the data can be explained by the corresponding variation between X and the the square line, Roughly five of the data cannot be explained by this, or rather five of variation cannot be explained by this. Finally, let's protect y for x equals 15 Plugging into white hat. We obtain y equals 1.35.

We are given a sample of data points X. Y. Listen to the top of this white board and we want to use this data to answer the questions A through F. As follows. And part A. On the left. We want to draw a scatter plot for these data points. I've already included a scatter plot and the data points X. Y. Are demarcated with the black crosses or exes Next in part B of the right. We want to compute the relevant some of this data as well as the Pearson correlation coefficient. R. I've already included the value of the sums as they are simply found by following these equations exactly. So some acts of some of the X values, some wise some of the Y values and so on. Next you complete. You are using the following formula which takes as input the sum to just computed as well as the sample size. And Plugged in gives r equals negative .973. Next for part C. Let's find the line of best fit. First. We have to find the X and Y means X by Y. Bar found by dividing by N. The sums for X and Y. Next we find the slope and intercept for the best fit line. Be. The slope is given by the formula here it takes its input N. And the sums computed above. So it's very similar to the correlation coefficient. R Plugging in to get equals negative .11 And plugging in b. x. bar and wine bar to a give us our intercept three producing line of best fit. Why Pat equals three minus 30.11 X. Next you were trying to scatter plot to plot. Ry hat we make sure to mark our ex me and what I mean, producing this. Next we go to the bottom right. For part E. We want to calculate the correlation coefficient or rather a court coefficient of determination. R squared, which is the square of the correlation coefficient and interpret its meaning. R Squared is simply .946. We interpret this to mean that 94.6 of variation in the data can be explained by the corresponding variation between X and the the square line, Roughly five of the data cannot be explained by this, or rather five of variation cannot be explained by this. Finally, let's protect y for x equals 15 Plugging into white hat. We obtain y equals 1.35.

This problem asks us to create graphs that represent flights between cities and then identify what type of graphs those are as a result of how they look. So, um, where I started with this was summarizing the given information, so I just kind of made myself a visual to the side. The way I set this up shows that there's four flights from Boston to New York to flights from New York to Boston and so forth. So there's lots of ways you could do that. But having that kind of summarized out to the side is gonna help me a lot. I also went ahead and already set up. All of my Vergis is. So when you're doing that, something you might want to think about when you're strategizing is thinking about what City has the most connections to the others. In this case, that's Newark. So I kinda situated that in the middle to help me have space. Most of all, a Z. I'm looking to connect those as we go through each part of this. There's subtle differences, and so you wanna be looking for keywords in the problem. Andi, as I went through those I just kind of summarized each also, so hopefully that'll help us as we go. Um, but let's go and start with a For part A. We wanted an edge between cities that have a flight between them in either direction was kind of a keyword there, telling us that direction does not matter on DSO. We want to connect each pair of cities that have flights between them, and this will be really simple. We see that Boston and New York have one on and New York and Miami, American, Detroit, American Washington and then Miami in Washington. So that's all we have to do for that one. As you're looking into the table to help you classify, we can notice that this is an undirected graph. It didn't matter what direction these were going in. It doesn't have multiple edges between Verdecia because we were just looking toe show the pair's and there's no loops. So this is a simple graph moving on to Part B. We want an edge in this case for each flight in either direction. So again, direction is not going to matter. This will be an undirected graph, but this time we want an edge, representing each flight. So each flight is definitely key. Word here, as I'm looking kind of to my summarized information over here, I know that there's going to be six total flights between Boston and Newark, 5 35 and one between each of those pairs of cities. And so I'm just trying to fit in six edges between Boston and work, which might be a tight squeeze. But we're going to do our best. Um, something that you want to keep in mind is your drawing these in, though, is that you do wanna leave space between each of the edges so that you can tell that there are multiple lines there. So that is five total between your work and Detroit's three right American Washington's five, then my me Washington just has one, um, again try to make. This is Nida's you can. But at the end of the day, you need to have the total number of flights between each city that number of artists, there's of edges. Excuse me. So we're looking Thio. Identify this. We have an undirected graph, but this time we have multiple edges between the verdict sees we still don't have any loops. And so this one is called a multi crap multi graph. Mhm. Yeah. So as we go forward curtsy had the exact same scenario is part beaded. Except now we're adding a sightseeing loop around Miami. So I'm just gonna drawing that I had on the last slide a little bit quicker this time. We're trying to you need them. So, six between New York and Boston, you need five here for me. Mind not one. Oops. That one between Miami and Washington Still, But now we're adding in a loop. And, of course, on a graph that just looks like a school. So something like that. Um, So we have the same scenario we're looking to classify again to undirected multiple edges between the verdict sees. But this time we do have loops. And so this one we will classify as a pseudo graph again. I'm using kind of the parameters that are given in that table for each of those so you can look it, um, those help you as you're classifying Part D says, um, in essence, that we need an edge from each origin city to each destination city. Um and so the key here is that direction does matter because it's telling us where we need to start and where we need to finish. Also, it doesn't say that we need one for each flight, though, So that's, um, telling us that we're not needing multiple edges like showing each flight. So as I'm looking to my summarized information, I know that there's flights from Boston to New York, so I need to show that on. We put these arrows in to show the direction, and then there's flights from New York to Boston. Mhm on. But of course there is. In the opposite direction is, um, same thing New York and Miami. They have flights in either direction. Same current Eric in Detroit, American Washington. Try your best to show what? Chinese air pointing also. Mhm. And last but not least, we have this one from Washington to Miami. Okay, you in Alright. So that's representing kind of all of the pairs again of origins and destinations this time. So, as we look to classify, we have directed graph because we included those arrows. Has, um it looks like multiple edges, so don't be tricked here. Um, this doesn't count as multiple edges in the sense of there's not multiple edges going in the same direction. So, um and there's no loops. It's the last thing that we're checking for each of these. So in that sense, this is going to be a simple directed graph again. Even though there's multiple edges between the Vergis sees, they are not in the same direction. So not counting as kind of representing the same thing. Our very last one here is very similar to D, but now we want toe say that there's an edge for each flight. So back Thio needing six between Boston and Newark child using. But the key here now is that the direction does matter. So we need Thio show show which direction each of these air going in. So let us do this for now. I think that's still clear which way that's going. So for pointing this direction to pointing from network from Newark to Boston between New York and Miami, we'll have five total and three air going from New York to Miami. Two are going from Miami to New York. Go back just a second ever believe in, Um and this is the way we're going Thio her scene So New York to Detroit has one Detroit to New York. Cast him New York Washington's 30. So the New York to Washington is three office attractions to and finally from Washington to Miami. Just have one. So as I'm drawing these arrows again, they're pointing in the direction that they're going, so hopefully that's pretty clear. And so, as we're looking to classify this last one, we do have a directed graph. We have multiple edges between the Verte sees in the sense that even multiple and going in the same direction, Um, and that's really the key here. There's no loops, obviously, but that's the defining characteristic is the multiple edges. So this one is going to be called a directed multi gra. You can see where the name came from, directed and multiple edges, and we're all set


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